{"file":[{"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2022_LinearAlgebra_Carlen.pdf","checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","relation":"main_file","success":1,"file_id":"12415","file_size":441184,"date_created":"2023-01-27T08:08:39Z","date_updated":"2023-01-27T08:08:39Z"}],"type":"journal_article","day":"01","month":"12","article_processing_charge":"Yes (via OA deal)","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2023-08-04T09:24:51Z","publication_status":"published","date_published":"2022-12-01T00:00:00Z","department":[{"_id":"JaMa"}],"abstract":[{"lang":"eng","text":"Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments."}],"oa":1,"oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2023-01-16T09:46:38Z","publisher":"Elsevier","scopus_import":"1","quality_controlled":"1","title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","status":"public","page":"289-310","doi":"10.1016/j.laa.2022.09.001","has_accepted_license":"1","author":[{"full_name":"Carlen, Eric A.","last_name":"Carlen","first_name":"Eric A."},{"last_name":"Zhang","first_name":"Haonan","full_name":"Zhang, Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"publication":"Linear Algebra and its Applications","external_id":{"isi":["000860689600014"]},"publication_identifier":{"issn":["0024-3795"]},"citation":{"short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","ama":"Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and its Applications</i>. 2022;654:289-310. doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>","apa":"Carlen, E. A., &#38; Zhang, H. (2022). Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","chicago":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>.","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” <i>Linear Algebra and its Applications</i>, vol. 654. Elsevier, pp. 289–310, 2022.","mla":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>, vol. 654, Elsevier, 2022, pp. 289–310, doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>."},"article_type":"original","language":[{"iso":"eng"}],"_id":"12216","intvolume":"       654","volume":654,"year":"2022","acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","isi":1,"keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"file_date_updated":"2023-01-27T08:08:39Z","ddc":["510"],"project":[{"grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis"}]}