三元算子环及其关联冯-诺依曼代数

arXiv - MATH - Operator Algebras Pub Date : 2024-07-14 DOI:arxiv-2407.10154

Liguang Wang, Ngai-Ching Wong

{"title":"三元算子环及其关联冯-诺依曼代数","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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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

摘要

在这篇短文中，我们证明了当且仅当一个冯-诺依曼代数不包含无邻直和时，它可以被写成一个 $W^\ast$-ternary ring of operators（简称 $W^\ast$-TRO）的连接冯-诺依曼代数。我们还为核TRO和$W^ast$-Exact TRO提供了一些新的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Ternary rings of operators and their linking von Neumann algebras

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Operator Algebras

自引率

0.00%

发文量