{"id":"https://openalex.org/W7204882348","doi":"https://doi.org/10.48550/arxiv.2608.30172","title":"Jensen' s trace inequality with equality condition and noncommutative Lamperti's theorem","display_name":"Jensen' s trace inequality with equality condition and noncommutative Lamperti's theorem","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204882348","doi":"https://doi.org/10.48550/arxiv.2608.30172"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30172","pdf_url":"https://arxiv.org/pdf/2608.30172","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.30172","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121301911","display_name":"Kai Fang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fang, Kai","raw_affiliation_strings":["Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , 150001 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , 150001 , China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153536532","display_name":"Xin He","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"He, Xin","raw_affiliation_strings":["Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , 150001 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , 150001 , China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5148938200","display_name":"Jinghao Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I134052481","display_name":"Harbin Normal University","ror":"https://ror.org/0270y6950","country_code":"CN","type":"education","lineage":["https://openalex.org/I134052481"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huang, Jinghao","raw_affiliation_strings":["Department of Mathematics , Harbin Normal University , Harbin , 150001 , China","Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , 150001 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Harbin Normal University , Harbin , 150001 , China","institution_ids":["https://openalex.org/I134052481"]},{"raw_affiliation_string":"Institute for Advanced Study in Mathematics of HIT , Harbin Institute of Technol- ogy , Harbin , 150001 , China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9092000126838684,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9092000126838684,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.0885000005364418,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.00139999995008111,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equality-conditions","display_name":"equality conditions","score":0.6029999852180481},{"id":"https://openalex.org/keywords/von-neumann-algebras","display_name":"von Neumann algebras","score":0.9139999747276306},{"id":"https://openalex.org/keywords/linear-isometries","display_name":"linear isometries","score":0.9819999933242798},{"id":"https://openalex.org/keywords/noncommutative-lp-spaces","display_name":"noncommutative Lp spaces","score":0.7300000190734863}],"concepts":[{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.9589999914169312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7979000210762024},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.7867000102996826},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.5927000045776367},{"id":"https://openalex.org/C153408630","wikidata":"https://www.wikidata.org/wiki/Q1970172","display_name":"Von Neumann algebra","level":3,"score":0.567300021648407},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5141000151634216},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5005000233650208},{"id":"https://openalex.org/C193645952","wikidata":"https://www.wikidata.org/wiki/Q7049219","display_name":"Noncommutative algebraic geometry","level":4,"score":0.4846000075340271},{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.42419999837875366},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35899999737739563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.329800009727478},{"id":"https://openalex.org/C29384965","wikidata":"https://www.wikidata.org/wiki/Q7049223","display_name":"Noncommutative quantum field theory","level":3,"score":0.3264000117778778},{"id":"https://openalex.org/C131229623","wikidata":"https://www.wikidata.org/wiki/Q977297","display_name":"Trace class","level":3,"score":0.3073999881744385},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2800000011920929}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30172","pdf_url":"https://arxiv.org/pdf/2608.30172","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.30172","doi":"https://doi.org/10.48550/arxiv.2608.30172","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30172","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30172","pdf_url":"https://arxiv.org/pdf/2608.30172","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204882348.pdf","grobid_xml":"https://content.openalex.org/works/W7204882348.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7171808923"],"related_works":["https://openalex.org/W7143402050","https://openalex.org/W1985366509","https://openalex.org/W1970362971","https://openalex.org/W4396672979","https://openalex.org/W1634511133","https://openalex.org/W7202203258","https://openalex.org/W2064609737","https://openalex.org/W2580762050","https://openalex.org/W2792167696","https://openalex.org/W2010593391"],"abstract_inverted_index":{"Let":[0],"$\\mathcal":[1],"M$":[2],"be":[3],"a":[4,11,62,71],"semifinite":[5,12],"von":[6],"Neumann":[7],"algebra":[8],"equipped":[9],"with":[10],"faithful":[13],"normal":[14],"trace":[15,20],"$\u03c4$.":[16],"We":[17],"establish":[18],"Jensen's":[19],"inequality":[21],"in":[22,35],"full":[23],"generality":[24],"and":[25,37,47],"characterize":[26,55],"its":[27],"equality":[28,49],"case,":[29],"which":[30,69],"answers":[31],"two":[32],"questions":[33],"raised":[34],"[Kosaki2013]":[36],"[HaradaKosaki2008].":[38],"As":[39],"an":[40],"application,":[41],"we":[42,54],"derive":[43],"noncommutative":[44,66,72],"Lamperti-type":[45],"inequalities":[46],"their":[48],"conditions.":[50],"Employing":[51],"this":[52],"result,":[53],"linear":[56,76],"isometries":[57],"(not":[58],"necessarily":[59],"surjective)":[60],"on":[61],"class":[63],"of":[64],"$F$-normed":[65],"Orlicz":[67],"spaces,":[68],"provides":[70],"Lamperti's":[73],"theorem":[74],"for":[75],"isometries.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}