{"title":"The Space of Tracial States on a C$^*$-Algebra","authors":"Bruce Blackadar, Mikael Rørdam","doi":"arxiv-2409.09644","DOIUrl":null,"url":null,"abstract":"We give a simple and elementary proof that the tracial state space of a\nunital C$^*$-algebra is a Choquet simplex, using the center-valued trace on a\nfinite von Neumann algebra.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09644","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We give a simple and elementary proof that the tracial state space of a
unital C$^*$-algebra is a Choquet simplex, using the center-valued trace on a
finite von Neumann algebra.
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