{"acknowledgement":"I am grateful to Boguslaw Zegarliński for asking me the questions in [3] and for helpful communication. I also want to thank Paata Ivanisvili for drawing [25] to my attention and for useful correspondence. Many thanks to the anonymous referee for the valuable comments and for pointing out some errors in an earlier version of the paper. This work is partially 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.","date_published":"2023-07-08T00:00:00Z","article_processing_charge":"No","title":"Some convexity and monotonicity results of trace functionals","quality_controlled":"1","type":"journal_article","_id":"13271","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.05785","open_access":"1"}],"doi":"10.1007/s00023-023-01345-7","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","publication_status":"epub_ahead","date_updated":"2023-12-13T11:33:46Z","status":"public","isi":1,"ec_funded":1,"publication_identifier":{"issn":["1424-0637"]},"citation":{"apa":"Zhang, H. (2023). Some convexity and monotonicity results of trace functionals. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-023-01345-7\">https://doi.org/10.1007/s00023-023-01345-7</a>","chicago":"Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-023-01345-7\">https://doi.org/10.1007/s00023-023-01345-7</a>.","short":"H. Zhang, Annales Henri Poincare (2023).","ista":"Zhang H. 2023. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare.","ama":"Zhang H. Some convexity and monotonicity results of trace functionals. <i>Annales Henri Poincare</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00023-023-01345-7\">10.1007/s00023-023-01345-7</a>","mla":"Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” <i>Annales Henri Poincare</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00023-023-01345-7\">10.1007/s00023-023-01345-7</a>.","ieee":"H. Zhang, “Some convexity and monotonicity results of trace functionals,” <i>Annales Henri Poincare</i>. Springer Nature, 2023."},"oa_version":"Preprint","abstract":[{"text":"In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s,\r\nfor parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems.","lang":"eng"}],"publication":"Annales Henri Poincare","oa":1,"date_created":"2023-07-23T22:01:15Z","external_id":{"isi":["001025709100001"],"arxiv":["2108.05785"]},"publisher":"Springer Nature","language":[{"iso":"eng"}],"author":[{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","full_name":"Zhang, Haonan","last_name":"Zhang"}],"year":"2023","day":"08","article_type":"original","month":"07","department":[{"_id":"JaMa"}],"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"},{"grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis"}]}