{"date_updated":"2023-06-28T11:54:35Z","language":[{"iso":"eng"}],"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).","volume":23,"file_date_updated":"2023-01-20T10:45:06Z","isi":1,"oa":1,"year":"2023","intvolume":"        23","publisher":"Springer Nature","has_accepted_license":"1","issue":"1","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","month":"01","status":"public","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>","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>","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.","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","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>.","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>."},"project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"doi":"10.1007/s00028-022-00859-7","_id":"12104","article_type":"original","quality_controlled":"1","publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"type":"journal_article","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2023-01-01T00:00:00Z","abstract":[{"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.","lang":"eng"}],"file":[{"file_id":"12325","creator":"dernst","file_size":422612,"access_level":"open_access","relation":"main_file","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","checksum":"1f34f3e2cb521033de6154f274ea3a4e","date_created":"2023-01-20T10:45:06Z","success":1,"date_updated":"2023-01-20T10:45:06Z","content_type":"application/pdf"}],"article_number":"9","article_processing_charge":"Yes (via OA deal)","author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870"},{"orcid":"0000-0002-0519-4241","last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"oa_version":"Published Version","scopus_import":"1","ddc":["510"],"publication":"Journal of Evolution Equations","publication_status":"published","external_id":{"isi":["000906214600004"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-01-08T23:00:53Z","department":[{"_id":"JaMa"}],"day":"01","ec_funded":1}