[{"article_type":"original","article_processing_charge":"Yes (via OA deal)","type":"journal_article","publication":"Potential Analysis","date_updated":"2025-12-15T13:11:24Z","PlanS_conform":"1","scopus_import":"1","ddc":["510"],"main_file_link":[{"url":"https://doi.org/10.1007/s11118-025-10251-y","open_access":"1"}],"ec_funded":1,"publication_status":"epub_ahead","doi":"10.1007/s11118-025-10251-y","year":"2025","volume":64,"title":"Boundary representations of intermediate forms between a regular Dirichlet form and its active main part","oa":1,"day":"03","OA_type":"hybrid","abstract":[{"text":"We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the sandwiched semigroups in terms of pairs consisting of an open set and a measure on an abstract boundary.","lang":"eng"}],"article_number":"6","language":[{"iso":"eng"}],"citation":{"mla":"Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>, vol. 64, 6, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>.","short":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis 64 (2025).","ista":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2025. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. Potential Analysis. 64, 6.","chicago":"Keller, Matthias, Daniel Lenz, Marcel Schmidt, Michael Schwarz, and Melchior Wirth. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>.","ieee":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, and M. Wirth, “Boundary representations of intermediate forms between a regular Dirichlet form and its active main part,” <i>Potential Analysis</i>, vol. 64. Springer Nature, 2025.","ama":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. 2025;64. doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>","apa":"Keller, M., Lenz, D., Schmidt, M., Schwarz, M., &#38; Wirth, M. (2025). Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>"},"publisher":"Springer Nature","department":[{"_id":"JaMa"}],"date_created":"2025-12-14T23:02:03Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"month":"12","status":"public","date_published":"2025-12-03T00:00:00Z","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}],"quality_controlled":"1","_id":"20814","intvolume":"        64","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"arxiv":1,"external_id":{"arxiv":["2301.01035"]},"author":[{"full_name":"Keller, Matthias","last_name":"Keller","first_name":"Matthias"},{"last_name":"Lenz","first_name":"Daniel","full_name":"Lenz, Daniel"},{"first_name":"Marcel","last_name":"Schmidt","full_name":"Schmidt, Marcel"},{"last_name":"Schwarz","first_name":"Michael","full_name":"Schwarz, Michael"},{"first_name":"Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241"}],"OA_place":"publisher","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","has_accepted_license":"1","acknowledgement":"Open Access funding enabled and organized by Projekt DEAL. The first three authors acknowledge financial support of the DFG within the priority programme Geometry at Infinity.\r\nM.W. acknowledges financial support by the German Academic Scholarship Foundation, by the Austrian Science Fund (FWF) through grant number F65 and the Esprit Programme [ESP 156], and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117)."},{"ddc":["510"],"scopus_import":"1","date_updated":"2025-09-30T12:19:22Z","publication":"Communications in Mathematical Physics","type":"journal_article","article_processing_charge":"Yes (via OA deal)","article_type":"original","article_number":"110","language":[{"iso":"eng"}],"abstract":[{"text":"We introduce operator-valued twisted Araki–Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes q-Gaussian and q-Araki–Woods algebras and also generalize Shlyakhtenko’s von Neumann algebras generated by operator-valued semicircular variables. We develop a disintegration theory that reduces the isomorphism type of operator-valued twisted Araki–Woods algebras over type I factors to the scalar-valued case. Moreover, these algebras come with a natural weight, and we characterize its modular theory. We also give sufficient criteria that guarantee the factoriality of these algebras.","lang":"eng"}],"corr_author":"1","OA_type":"hybrid","day":"01","oa":1,"title":"Operator-valued twisted Araki–Woods algebras","volume":406,"year":"2025","doi":"10.1007/s00220-025-05285-7","publication_status":"published","file_date_updated":"2025-05-05T09:20:54Z","intvolume":"       406","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"issue":"5","_id":"19625","quality_controlled":"1","project":[{"name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N"}],"date_published":"2025-05-01T00:00:00Z","status":"public","month":"05","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"date_created":"2025-04-27T22:02:13Z","department":[{"_id":"JaMa"}],"citation":{"chicago":"Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00220-025-05285-7\">https://doi.org/10.1007/s00220-025-05285-7</a>.","short":"R.R. Kumar, M. Wirth, Communications in Mathematical Physics 406 (2025).","mla":"Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5, 110, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-025-05285-7\">10.1007/s00220-025-05285-7</a>.","ista":"Kumar RR, Wirth M. 2025. Operator-valued twisted Araki–Woods algebras. Communications in Mathematical Physics. 406(5), 110.","ama":"Kumar RR, Wirth M. Operator-valued twisted Araki–Woods algebras. <i>Communications in Mathematical Physics</i>. 2025;406(5). doi:<a href=\"https://doi.org/10.1007/s00220-025-05285-7\">10.1007/s00220-025-05285-7</a>","ieee":"R. R. Kumar and M. Wirth, “Operator-valued twisted Araki–Woods algebras,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5. Springer Nature, 2025.","apa":"Kumar, R. R., &#38; Wirth, M. (2025). Operator-valued twisted Araki–Woods algebras. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-025-05285-7\">https://doi.org/10.1007/s00220-025-05285-7</a>"},"publisher":"Springer Nature","acknowledgement":"The authors want to thank the organizers of YMC*A 2023 in Leuven, where this collaboration was conceived. They are grateful to Dan Voiculescu for a valuable historical remark and to Zhiyuan Yang for raising the question if operator-valued weights give rise to Tomita correspondences. R.K. was funded by IIT Kanpur through the Institute Postdoctoral Fellowship. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.\r\nOpen Access funding enabled and organized by Projekt DEAL.","has_accepted_license":"1","file":[{"relation":"main_file","access_level":"open_access","date_created":"2025-05-05T09:20:54Z","file_size":650764,"success":1,"checksum":"2948e8f567f20f5f837061d2c775534f","file_name":"2025_CommMathPhysics_Kumar.pdf","file_id":"19650","date_updated":"2025-05-05T09:20:54Z","content_type":"application/pdf","creator":"dernst"}],"oa_version":"Published Version","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"OA_place":"publisher","author":[{"last_name":"Kumar","first_name":"R. Rahul","full_name":"Kumar, R. Rahul"},{"orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","first_name":"Melchior"}],"pmid":1,"external_id":{"arxiv":["2406.06179"],"pmid":["40225194"],"isi":["001464170400003"]},"arxiv":1},{"date_published":"2024-07-01T00:00:00Z","quality_controlled":"1","project":[{"grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}],"_id":"18900","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"issue":"14","intvolume":"      2024","publisher":"Oxford University Press","citation":{"ama":"Wirth M. Modular completely Dirichlet forms as squares of derivations. <i>International Mathematics Research Notices</i>. 2024;2024(14):10597-10614. doi:<a href=\"https://doi.org/10.1093/imrn/rnae092\">10.1093/imrn/rnae092</a>","apa":"Wirth, M. (2024). Modular completely Dirichlet forms as squares of derivations. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae092\">https://doi.org/10.1093/imrn/rnae092</a>","ieee":"M. Wirth, “Modular completely Dirichlet forms as squares of derivations,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 14. Oxford University Press, pp. 10597–10614, 2024.","ista":"Wirth M. 2024. Modular completely Dirichlet forms as squares of derivations. International Mathematics Research Notices. 2024(14), 10597–10614.","short":"M. Wirth, International Mathematics Research Notices 2024 (2024) 10597–10614.","mla":"Wirth, Melchior. “Modular Completely Dirichlet Forms as Squares of Derivations.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 14, Oxford University Press, 2024, pp. 10597–614, doi:<a href=\"https://doi.org/10.1093/imrn/rnae092\">10.1093/imrn/rnae092</a>.","chicago":"Wirth, Melchior. “Modular Completely Dirichlet Forms as Squares of Derivations.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae092\">https://doi.org/10.1093/imrn/rnae092</a>."},"department":[{"_id":"JaMa"}],"date_created":"2025-01-27T12:36:10Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"page":"10597-10614","month":"07","status":"public","file":[{"creator":"dernst","content_type":"application/pdf","file_id":"18901","date_updated":"2025-01-27T12:38:10Z","success":1,"file_size":689984,"checksum":"3e1f80d58ada0c60a58f35df8080967e","file_name":"2024_IMRN_Wirth.pdf","date_created":"2025-01-27T12:38:10Z","relation":"main_file","access_level":"open_access"}],"has_accepted_license":"1","acknowledgement":"The author was funded by the Austrian Science Fund under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. ","external_id":{"isi":["001222279400001"]},"author":[{"orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth"}],"isi":1,"OA_place":"publisher","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","type":"journal_article","publication":"International Mathematics Research Notices","date_updated":"2025-09-09T12:02:46Z","scopus_import":"1","ddc":["510"],"article_type":"original","article_processing_charge":"Yes (via OA deal)","year":"2024","title":"Modular completely Dirichlet forms as squares of derivations","volume":2024,"oa":1,"day":"01","OA_type":"hybrid","abstract":[{"lang":"eng","text":"We prove that certain closable derivations on the GNS Hilbert space associated with a non-tracial weight on a von Neumann algebra give rise to GNS-symmetric semigroups of contractive completely positive maps on the von Neumann algebra."}],"corr_author":"1","language":[{"iso":"eng"}],"file_date_updated":"2025-01-27T12:38:10Z","publication_status":"published","doi":"10.1093/imrn/rnae092"},{"scopus_import":"1","ddc":["510"],"type":"journal_article","publication":"Communications in Mathematical Physics","date_updated":"2025-09-04T13:50:22Z","article_processing_charge":"Yes (via OA deal)","article_type":"original","article_number":"95","language":[{"iso":"eng"}],"corr_author":"1","abstract":[{"text":"We extend three related results from the analysis of influences of Boolean functions to the quantum setting, namely the KKL theorem, Friedgut’s Junta theorem and Talagrand’s variance inequality for geometric influences. Our results are derived by a joint use of recently studied hypercontractivity and gradient estimates. These generic tools also allow us to derive generalizations of these results in a general von Neumann algebraic setting beyond the case of the quantum hypercube, including examples in infinite dimensions relevant to quantum information theory such as continuous variables quantum systems. Finally, we comment on the implications of our results as regards to noncommutative extensions of isoperimetric type inequalities, quantum circuit complexity lower bounds and the learnability of quantum observables.","lang":"eng"}],"oa":1,"day":"09","year":"2024","title":"Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions","volume":405,"doi":"10.1007/s00220-024-04981-0","publication_status":"published","file_date_updated":"2024-05-06T06:18:45Z","_id":"15350","issue":"4","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"intvolume":"       405","quality_controlled":"1","project":[{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"date_published":"2024-04-09T00:00:00Z","month":"04","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"department":[{"_id":"JaMa"}],"date_created":"2024-04-29T08:47:28Z","citation":{"chicago":"Rouzé, Cambyse, Melchior Wirth, and Haonan Zhang. “Quantum Talagrand, KKL and Friedgut’s Theorems and the Learnability of Quantum Boolean Functions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00220-024-04981-0\">https://doi.org/10.1007/s00220-024-04981-0</a>.","ista":"Rouzé C, Wirth M, Zhang H. 2024. Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions. Communications in Mathematical Physics. 405(4), 95.","short":"C. Rouzé, M. Wirth, H. Zhang, Communications in Mathematical Physics 405 (2024).","mla":"Rouzé, Cambyse, et al. “Quantum Talagrand, KKL and Friedgut’s Theorems and the Learnability of Quantum Boolean Functions.” <i>Communications in Mathematical Physics</i>, vol. 405, no. 4, 95, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00220-024-04981-0\">10.1007/s00220-024-04981-0</a>.","ieee":"C. Rouzé, M. Wirth, and H. Zhang, “Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions,” <i>Communications in Mathematical Physics</i>, vol. 405, no. 4. Springer Nature, 2024.","ama":"Rouzé C, Wirth M, Zhang H. Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions. <i>Communications in Mathematical Physics</i>. 2024;405(4). doi:<a href=\"https://doi.org/10.1007/s00220-024-04981-0\">10.1007/s00220-024-04981-0</a>","apa":"Rouzé, C., Wirth, M., &#38; Zhang, H. (2024). Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-024-04981-0\">https://doi.org/10.1007/s00220-024-04981-0</a>"},"publisher":"Springer Nature","file":[{"creator":"dernst","content_type":"application/pdf","file_id":"15365","date_updated":"2024-05-06T06:18:45Z","file_name":"2024_CommMathPhysics_Rouze.pdf","file_size":653676,"checksum":"8ecd168755f0d40ebd7cd0b71063acfc","success":1,"date_created":"2024-05-06T06:18:45Z","access_level":"open_access","relation":"main_file"}],"has_accepted_license":"1","acknowledgement":"Open access funding provided by the Carolinas Consortium.\r\nH.Z. is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. H.Z. would like to thank the American Institute of Mathematics and the AIM workshop Analysis on the hypercube with applications to quantum computing. He is also grateful to the organizers and other participants for creating an active atmosphere. The research of C.R. has been supported by ANR project QTraj (ANR-20-CE40-0024-01) of the French National Research Agency (ANR). C.R. acknowledges the support of the Munich Center for Quantum Sciences and Technology, as well as the Humboldt Foundation. C.R. would like to thank Amanda Young for fruitful discussion on the applications of Friedgut’s Junta theorem to learning quantum dynamics. The research of M.W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. The authors want to thank Francisco Escudero Gutierrez and Hsin-Yuan Huang for helpful comments on an earlier version of the paper. They are grateful to the referees for the careful reading and helpful comments.","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","isi":1,"external_id":{"isi":["001199509500004"],"pmid":["38606337"],"arxiv":["2209.07279"]},"arxiv":1,"pmid":1,"author":[{"last_name":"Rouzé","first_name":"Cambyse","full_name":"Rouzé, Cambyse"},{"full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","first_name":"Melchior","last_name":"Wirth"},{"first_name":"Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}]},{"publication_status":"published","doi":"10.1016/j.jfa.2024.110475","file_date_updated":"2025-01-09T09:33:56Z","abstract":[{"text":"In this article we prove a refined version of the Christensen–Evans theorem for generators of uniformly continuous GNS-symmetric quantum Markov semigroups. We use this result to show the existence of GNS-symmetric extensions of GNS-symmetric quantum Markov semigroups. In particular, this implies that the generators of GNS-symmetric quantum Markov semigroups on finite-dimensional von Neumann algebra can be written in the form specified by Alicki's theorem.","lang":"eng"}],"corr_author":"1","language":[{"iso":"eng"}],"article_number":"110475","volume":287,"title":"Christensen–Evans theorem and extensions of GNS-symmetric quantum Markov semigroups","year":"2024","day":"01","OA_type":"hybrid","oa":1,"article_type":"original","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"scopus_import":"1","date_updated":"2025-09-08T07:24:07Z","publication":"Journal of Functional Analysis","type":"journal_article","oa_version":"Published Version","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"last_name":"Wirth","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241"}],"external_id":{"isi":["001237916800001"]},"OA_place":"publisher","isi":1,"has_accepted_license":"1","file":[{"creator":"dernst","content_type":"application/pdf","date_updated":"2025-01-09T09:33:56Z","file_id":"18802","file_name":"2024_JourFunctAnalysis_Wirth.pdf","checksum":"657c9f77dd30bb31ce43a591f58126a2","success":1,"file_size":503148,"date_created":"2025-01-09T09:33:56Z","access_level":"open_access","relation":"main_file"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","month":"08","citation":{"apa":"Wirth, M. (2024). Christensen–Evans theorem and extensions of GNS-symmetric quantum Markov semigroups. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110475\">https://doi.org/10.1016/j.jfa.2024.110475</a>","ama":"Wirth M. Christensen–Evans theorem and extensions of GNS-symmetric quantum Markov semigroups. <i>Journal of Functional Analysis</i>. 2024;287(3). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110475\">10.1016/j.jfa.2024.110475</a>","ieee":"M. Wirth, “Christensen–Evans theorem and extensions of GNS-symmetric quantum Markov semigroups,” <i>Journal of Functional Analysis</i>, vol. 287, no. 3. Elsevier, 2024.","chicago":"Wirth, Melchior. “Christensen–Evans Theorem and Extensions of GNS-Symmetric Quantum Markov Semigroups.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110475\">https://doi.org/10.1016/j.jfa.2024.110475</a>.","ista":"Wirth M. 2024. Christensen–Evans theorem and extensions of GNS-symmetric quantum Markov semigroups. Journal of Functional Analysis. 287(3), 110475.","short":"M. Wirth, Journal of Functional Analysis 287 (2024).","mla":"Wirth, Melchior. “Christensen–Evans Theorem and Extensions of GNS-Symmetric Quantum Markov Semigroups.” <i>Journal of Functional Analysis</i>, vol. 287, no. 3, 110475, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110475\">10.1016/j.jfa.2024.110475</a>."},"publisher":"Elsevier","date_created":"2024-05-12T22:01:01Z","department":[{"_id":"JaMa"}],"intvolume":"       287","issue":"3","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"_id":"15373","date_published":"2024-08-01T00:00:00Z","quality_controlled":"1"},{"abstract":[{"lang":"eng","text":"Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups."}],"corr_author":"1","language":[{"iso":"eng"}],"title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","volume":24,"year":"2023","day":"01","oa":1,"publication_status":"published","doi":"10.1007/s00023-022-01220-x","ec_funded":1,"file_date_updated":"2023-08-14T11:38:28Z","ddc":["510"],"scopus_import":"1","date_updated":"2025-04-23T08:53:05Z","type":"journal_article","publication":"Annales Henri Poincare","article_type":"original","article_processing_charge":"Yes (via OA deal)","acknowledgement":"H.Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117) and from the Austrian Science Fund (FWF) through grant number F65. Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. Open access funding provided by Austrian Science Fund (FWF).","has_accepted_license":"1","file":[{"file_id":"14051","date_updated":"2023-08-14T11:38:28Z","creator":"dernst","content_type":"application/pdf","date_created":"2023-08-14T11:38:28Z","relation":"main_file","access_level":"open_access","success":1,"checksum":"8c7b185eba5ccd92ef55c120f654222c","file_size":554871,"file_name":"2023_AnnalesHenriPoincare_Wirth.pdf"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"author":[{"last_name":"Wirth","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior"},{"first_name":"Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}],"external_id":{"isi":["000837499800002"],"pmid":["36950223"],"arxiv":["2105.08303"]},"arxiv":1,"isi":1,"intvolume":"        24","publication_identifier":{"issn":["1424-0637"]},"_id":"12087","date_published":"2023-03-01T00:00:00Z","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"},{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"quality_controlled":"1","page":"717-750","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","month":"03","citation":{"ama":"Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. 2023;24:717-750. doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>","ieee":"M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 717–750, 2023.","apa":"Wirth, M., &#38; Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>","chicago":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>.","short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","mla":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 717–50, doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>.","ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750."},"publisher":"Springer Nature","date_created":"2022-09-11T22:01:57Z","department":[{"_id":"JaMa"}]},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"status":"public","month":"01","publisher":"Springer Nature","citation":{"ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. 2023;23(1). doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” <i>Journal of Evolution Equations</i>, vol. 23, no. 1. Springer Nature, 2023.","apa":"Dello Schiavo, L., &#38; Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>, vol. 23, no. 1, 9, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>."},"department":[{"_id":"JaMa"}],"date_created":"2023-01-08T23:00:53Z","publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"issue":"1","intvolume":"        23","_id":"12104","date_published":"2023-01-01T00:00:00Z","quality_controlled":"1","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"author":[{"last_name":"Dello Schiavo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"},{"full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior"}],"external_id":{"pmid":["36597554"],"isi":["000906214600004"]},"isi":1,"acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","has_accepted_license":"1","file":[{"creator":"dernst","content_type":"application/pdf","date_updated":"2023-01-20T10:45:06Z","file_id":"12325","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","file_size":422612,"success":1,"checksum":"1f34f3e2cb521033de6154f274ea3a4e","date_created":"2023-01-20T10:45:06Z","access_level":"open_access","relation":"main_file"}],"article_type":"original","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"scopus_import":"1","date_updated":"2025-04-23T08:45:56Z","type":"journal_article","publication":"Journal of Evolution Equations","publication_status":"published","doi":"10.1007/s00028-022-00859-7","ec_funded":1,"file_date_updated":"2023-01-20T10:45:06Z","corr_author":"1","abstract":[{"lang":"eng","text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces."}],"article_number":"9","language":[{"iso":"eng"}],"title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","volume":23,"year":"2023","day":"01","oa":1},{"article_type":"original","article_processing_charge":"No","date_updated":"2024-10-09T21:05:50Z","type":"journal_article","publication":"Proceedings of the American Mathematical Society","scopus_import":"1","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1804.08353","open_access":"1"}],"publication_status":"published","doi":"10.1090/proc/14361","title":"Sobolev-type inequalities and eigenvalue growth on graphs with finite measure","volume":151,"year":"2023","day":"01","oa":1,"corr_author":"1","abstract":[{"lang":"eng","text":"In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established."}],"language":[{"iso":"eng"}],"publisher":"American Mathematical Society","citation":{"ama":"Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American Mathematical Society</i>. 2023;151(8):3401-3414. doi:<a href=\"https://doi.org/10.1090/proc/14361\">10.1090/proc/14361</a>","apa":"Hua, B., Keller, M., Schwarz, M., &#38; Wirth, M. (2023). Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/14361\">https://doi.org/10.1090/proc/14361</a>","ieee":"B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and eigenvalue growth on graphs with finite measure,” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 8. American Mathematical Society, pp. 3401–3414, 2023.","short":"B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical Society 151 (2023) 3401–3414.","mla":"Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:<a href=\"https://doi.org/10.1090/proc/14361\">10.1090/proc/14361</a>.","ista":"Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 151(8), 3401–3414.","chicago":"Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2023. <a href=\"https://doi.org/10.1090/proc/14361\">https://doi.org/10.1090/proc/14361</a>."},"date_created":"2023-07-02T22:00:43Z","department":[{"_id":"JaMa"}],"page":"3401-3414","status":"public","month":"08","date_published":"2023-08-01T00:00:00Z","quality_controlled":"1","issue":"8","intvolume":"       151","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"_id":"13177","author":[{"first_name":"Bobo","last_name":"Hua","full_name":"Hua, Bobo"},{"full_name":"Keller, Matthias","first_name":"Matthias","last_name":"Keller"},{"full_name":"Schwarz, Michael","last_name":"Schwarz","first_name":"Michael"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","last_name":"Wirth","first_name":"Melchior"}],"external_id":{"isi":["000988204400001"],"arxiv":["1804.08353"]},"arxiv":1,"isi":1,"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The second author was supported by the priority program SPP2026 of the German Research Foundation (DFG). The fourth author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2."},{"file":[{"date_created":"2024-01-30T12:15:11Z","relation":"main_file","access_level":"open_access","success":1,"file_size":481209,"checksum":"cca204e81891270216a0c84eb8bcd398","file_name":"2023_CommMathPhysics_Vernooij.pdf","file_id":"14905","date_updated":"2024-01-30T12:15:11Z","creator":"dernst","content_type":"application/pdf"}],"has_accepted_license":"1","acknowledgement":"The authors are grateful to Martijn Caspers for helpful comments on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. Open access funding provided by Austrian Science Fund (FWF).","isi":1,"arxiv":1,"external_id":{"arxiv":["2303.15949"],"pmid":["37766789"],"isi":["001033655400002"]},"author":[{"full_name":"Vernooij, Matthijs","last_name":"Vernooij","first_name":"Matthijs"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth"}],"pmid":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","project":[{"name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N"}],"quality_controlled":"1","date_published":"2023-10-01T00:00:00Z","_id":"13319","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"intvolume":"       403","date_created":"2023-07-30T22:01:03Z","department":[{"_id":"JaMa"}],"publisher":"Springer Nature","citation":{"apa":"Vernooij, M., &#38; Wirth, M. (2023). Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>","ieee":"M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 403. Springer Nature, pp. 381–416, 2023.","ama":"Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2023;403:381-416. doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>","short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","mla":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 403, Springer Nature, 2023, pp. 381–416, doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>.","ista":"Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 381–416.","chicago":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>."},"month":"10","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"page":"381-416","oa":1,"day":"01","year":"2023","title":"Derivations and KMS-symmetric quantum Markov semigroups","volume":403,"language":[{"iso":"eng"}],"corr_author":"1","abstract":[{"text":"We prove that the generator of the L2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule.","lang":"eng"}],"file_date_updated":"2024-01-30T12:15:11Z","doi":"10.1007/s00220-023-04795-6","publication_status":"published","type":"journal_article","publication":"Communications in Mathematical Physics","date_updated":"2025-04-23T13:10:45Z","scopus_import":"1","ddc":["510"],"article_processing_charge":"Yes (via OA deal)","article_type":"original"},{"publisher":"Springer Nature","citation":{"ieee":"M. Wirth, “Kac regularity and domination of quadratic forms,” <i>Advances in Operator Theory</i>, vol. 7, no. 3. Springer Nature, 2022.","ama":"Wirth M. Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. 2022;7(3). doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>","apa":"Wirth, M. (2022). Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>","ista":"Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 7(3), 38.","short":"M. Wirth, Advances in Operator Theory 7 (2022).","mla":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>, vol. 7, no. 3, 38, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>.","chicago":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>."},"date_created":"2022-08-18T07:22:24Z","department":[{"_id":"JaMa"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"month":"07","status":"public","date_published":"2022-07-01T00:00:00Z","quality_controlled":"1","_id":"11916","publication_identifier":{"eissn":["2538-225X"]},"intvolume":"         7","issue":"3","author":[{"first_name":"Melchior","last_name":"Wirth","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"file_id":"11921","date_updated":"2022-08-18T08:02:34Z","content_type":"application/pdf","creator":"dernst","relation":"main_file","access_level":"open_access","date_created":"2022-08-18T08:02:34Z","success":1,"checksum":"913474844a1b38264fb710746d5e2e98","file_size":389060,"file_name":"2022_AdvancesOperatorTheory_Wirth.pdf"}],"acknowledgement":"The author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement during the author’s ongoing graduate studies and him as well as Marcel Schmidt for fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu and Peter Stollmann for valuable comments on a preliminary version of this article. He would also like to thank the organizers of the conference Analysis and Geometry on Graphs and Manifolds in Potsdam, where the initial motivation of this article was conceived, and the organizers of the intense activity period Metric Measure Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","has_accepted_license":"1","keyword":["Algebra and Number Theory","Analysis"],"article_type":"original","article_processing_charge":"Yes (via OA deal)","type":"journal_article","publication":"Advances in Operator Theory","date_updated":"2024-10-09T21:03:07Z","scopus_import":"1","ddc":["510"],"file_date_updated":"2022-08-18T08:02:34Z","publication_status":"published","doi":"10.1007/s43036-022-00199-w","year":"2022","volume":7,"title":"Kac regularity and domination of quadratic forms","oa":1,"day":"01","corr_author":"1","abstract":[{"lang":"eng","text":"A domain is called Kac regular for a quadratic form on L2 if every functions vanishing almost everywhere outside the domain can be approximated in form norm by functions with compact support in the domain. It is shown that this notion is stable under domination of quadratic forms. As applications measure perturbations of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and Schrödinger operators on manifolds are studied. Along the way a characterization of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally Riemannian metric measure spaces is obtained."}],"language":[{"iso":"eng"}],"article_number":"38"},{"date_published":"2022-04-08T00:00:00Z","quality_controlled":"1","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"_id":"11330","intvolume":"       187","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"issue":"2","publisher":"Springer Nature","citation":{"ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” <i>Journal of Statistical Physics</i>, vol. 187, no. 2. Springer Nature, 2022.","ama":"Wirth M. A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. 2022;187(2). doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>","apa":"Wirth, M. (2022). A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>","ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.","mla":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>, vol. 187, no. 2, 19, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>.","short":"M. Wirth, Journal of Statistical Physics 187 (2022).","chicago":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>."},"date_created":"2022-04-24T22:01:43Z","department":[{"_id":"JaMa"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"month":"04","status":"public","file":[{"creator":"dernst","content_type":"application/pdf","file_id":"11338","date_updated":"2022-04-29T11:24:23Z","file_name":"2022_JourStatisticalPhysics_Wirth.pdf","success":1,"checksum":"f3e0b00884b7dde31347a3756788b473","file_size":362119,"date_created":"2022-04-29T11:24:23Z","access_level":"open_access","relation":"main_file"}],"has_accepted_license":"1","acknowledgement":"The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","external_id":{"pmid":["35509951"],"isi":["000780305000001"]},"pmid":1,"author":[{"last_name":"Wirth","first_name":"Melchior","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","publication":"Journal of Statistical Physics","type":"journal_article","date_updated":"2025-06-12T06:17:37Z","scopus_import":"1","ddc":["510","530"],"article_type":"original","article_processing_charge":"Yes (via OA deal)","year":"2022","volume":187,"title":"A dual formula for the noncommutative transport distance","oa":1,"day":"08","abstract":[{"text":"In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation.","lang":"eng"}],"corr_author":"1","language":[{"iso":"eng"}],"article_number":"19","ec_funded":1,"file_date_updated":"2022-04-29T11:24:23Z","publication_status":"published","doi":"10.1007/s10955-022-02911-9"},{"article_type":"original","article_processing_charge":"No","date_updated":"2025-06-25T07:41:05Z","publication":"Journal of Functional Analysis","type":"journal_article","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.1016/j.jfa.2020.108848","open_access":"1"}],"publication_status":"published","doi":"10.1016/j.jfa.2020.108848","title":"Uniqueness of form extensions and domination of semigroups","volume":280,"year":"2021","OA_type":"free access","day":"15","oa":1,"abstract":[{"text":"In this article, we study uniqueness of form extensions in a rather general setting. The method is based on the theory of ordered Hilbert spaces and the concept of domination of semigroups. Our main abstract result transfers uniqueness of form extension of a dominating form to that of a dominated form. This result can be applied to a multitude of examples including various magnetic Schrödinger forms on graphs and on manifolds.","lang":"eng"}],"corr_author":"1","article_number":"108848","language":[{"iso":"eng"}],"publisher":"Elsevier","citation":{"mla":"Lenz, Daniel, et al. “Uniqueness of Form Extensions and Domination of Semigroups.” <i>Journal of Functional Analysis</i>, vol. 280, no. 6, 108848, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108848\">10.1016/j.jfa.2020.108848</a>.","short":"D. Lenz, M. Schmidt, M. Wirth, Journal of Functional Analysis 280 (2021).","ista":"Lenz D, Schmidt M, Wirth M. 2021. Uniqueness of form extensions and domination of semigroups. Journal of Functional Analysis. 280(6), 108848.","chicago":"Lenz, Daniel, Marcel Schmidt, and Melchior Wirth. “Uniqueness of Form Extensions and Domination of Semigroups.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2020.108848\">https://doi.org/10.1016/j.jfa.2020.108848</a>.","ieee":"D. Lenz, M. Schmidt, and M. Wirth, “Uniqueness of form extensions and domination of semigroups,” <i>Journal of Functional Analysis</i>, vol. 280, no. 6. Elsevier, 2021.","apa":"Lenz, D., Schmidt, M., &#38; Wirth, M. (2021). Uniqueness of form extensions and domination of semigroups. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108848\">https://doi.org/10.1016/j.jfa.2020.108848</a>","ama":"Lenz D, Schmidt M, Wirth M. Uniqueness of form extensions and domination of semigroups. <i>Journal of Functional Analysis</i>. 2021;280(6). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108848\">10.1016/j.jfa.2020.108848</a>"},"date_created":"2024-04-03T07:24:57Z","department":[{"_id":"JaMa"}],"status":"public","month":"03","date_published":"2021-03-15T00:00:00Z","quality_controlled":"1","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"intvolume":"       280","issue":"6","_id":"15261","author":[{"first_name":"Daniel","last_name":"Lenz","full_name":"Lenz, Daniel"},{"last_name":"Schmidt","first_name":"Marcel","full_name":"Schmidt, Marcel"},{"orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","first_name":"Melchior"}],"OA_place":"publisher","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["Analysis"]},{"language":[{"iso":"eng"}],"corr_author":"1","abstract":[{"lang":"eng","text":"We compute the deficiency spaces of operators of the form 𝐻𝐴⊗̂ 𝐼+𝐼⊗̂ 𝐻𝐵, for symmetric 𝐻𝐴 and self-adjoint 𝐻𝐵. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of 𝐻𝐵 having discrete, non-degenerate spectrum."}],"oa":1,"day":"01","year":"2021","volume":64,"title":"Self-adjoint extensions of bipartite Hamiltonians","doi":"10.1017/S0013091521000080","publication_status":"published","main_file_link":[{"url":"https://doi.org/10.1017/S0013091521000080","open_access":"1"}],"scopus_import":"1","type":"journal_article","publication":"Proceedings of the Edinburgh Mathematical Society","date_updated":"2024-10-09T21:05:06Z","article_processing_charge":"No","article_type":"original","acknowledgement":"M. W. gratefully acknowledges financial support by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA GmbH for their financial support in the form of scholarships during his Master's and Bachelor's studies respectively. The authors want to thank Mark Malamud for pointing out the reference [1] to them. This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","isi":1,"external_id":{"arxiv":["1912.03670"],"isi":["000721363700003"]},"arxiv":1,"author":[{"full_name":"Lenz, Daniel","last_name":"Lenz","first_name":"Daniel"},{"last_name":"Weinmann","first_name":"Timon","full_name":"Weinmann, Timon"},{"last_name":"Wirth","first_name":"Melchior","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"_id":"9627","intvolume":"        64","publication_identifier":{"issn":["0013-0915"],"eissn":["1464-3839"]},"issue":"3","quality_controlled":"1","date_published":"2021-08-01T00:00:00Z","month":"08","status":"public","page":"443-447","date_created":"2021-07-04T22:01:24Z","department":[{"_id":"JaMa"}],"citation":{"chicago":"Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/S0013091521000080\">https://doi.org/10.1017/S0013091521000080</a>.","ista":"Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.","short":"D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447.","mla":"Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 64, no. 3, Cambridge University Press, 2021, pp. 443–47, doi:<a href=\"https://doi.org/10.1017/S0013091521000080\">10.1017/S0013091521000080</a>.","apa":"Lenz, D., Weinmann, T., &#38; Wirth, M. (2021). Self-adjoint extensions of bipartite Hamiltonians. <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S0013091521000080\">https://doi.org/10.1017/S0013091521000080</a>","ama":"Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians. <i>Proceedings of the Edinburgh Mathematical Society</i>. 2021;64(3):443-447. doi:<a href=\"https://doi.org/10.1017/S0013091521000080\">10.1017/S0013091521000080</a>","ieee":"D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021."},"publisher":"Cambridge University Press"},{"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"file":[{"date_created":"2021-09-08T07:34:24Z","access_level":"open_access","relation":"main_file","file_name":"2021_CommunMathPhys_Wirth.pdf","checksum":"8a602f916b1c2b0dc1159708b7cb204b","file_size":505971,"file_id":"9990","date_updated":"2021-09-08T09:46:34Z","creator":"cchlebak","content_type":"application/pdf"}],"acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","isi":1,"arxiv":1,"external_id":{"pmid":["34776525"],"arxiv":["2007.13506"],"isi":["000691214200001"]},"pmid":1,"author":[{"first_name":"Melchior","last_name":"Wirth","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior"},{"last_name":"Zhang","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan"}],"_id":"9973","intvolume":"       387","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"quality_controlled":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"date_published":"2021-08-30T00:00:00Z","month":"08","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"page":"761–791","department":[{"_id":"JaMa"}],"date_created":"2021-08-30T10:07:44Z","publisher":"Springer Nature","citation":{"ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 387, Springer Nature, 2021, pp. 761–791, doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>.","chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>.","ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2021;387:761–791. doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>","apa":"Wirth, M., &#38; Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>","ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 387. Springer Nature, pp. 761–791, 2021."},"language":[{"iso":"eng"}],"corr_author":"1","abstract":[{"lang":"eng","text":"In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors."}],"oa":1,"day":"30","year":"2021","volume":387,"title":"Complete gradient estimates of quantum Markov semigroups","doi":"10.1007/s00220-021-04199-4","publication_status":"published","file_date_updated":"2021-09-08T09:46:34Z","ec_funded":1,"scopus_import":"1","ddc":["621"],"publication":"Communications in Mathematical Physics","type":"journal_article","date_updated":"2025-06-12T06:30:13Z","article_processing_charge":"Yes (via OA deal)","article_type":"original"}]