{"title":"Ternary rings of operators and their linking von Neumann algebras","authors":"Liguang Wang, Ngai-Ching Wong","doi":"arxiv-2407.10154","DOIUrl":null,"url":null,"abstract":"In this short note, we show that a von Neumann algebra can be written as the\nlinking von Neumann algebra of a $W^\\ast$-ternary ring of operators\n($W^\\ast$-TRO, in short), if and only if, it contains no abelian direct\nsummand. We also provide some new characterizations for nuclear TROs and\n$W^\\ast$-exact TROs.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-14","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-2407.10154","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
In this short note, we show that a von Neumann algebra can be written as the
linking von Neumann algebra of a $W^\ast$-ternary ring of operators
($W^\ast$-TRO, in short), if and only if, it contains no abelian direct
summand. We also provide some new characterizations for nuclear TROs and
$W^\ast$-exact TROs.
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