{"title":"C$^*$ 代数上的三态空间","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":"{\"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}","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
摘要
我们利用无穷 von Neumann 代数上的中心值迹，给出了一个简单而基本的证明，即无穷 C$^*$ 代数的三态空间是一个 Choquet 单纯形。
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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