{"title":"Toeplitz CAR流和I型分解","authors":"Masaki Izumi, R. Srinivasan","doi":"10.1215/0023608X-2009-001","DOIUrl":null,"url":null,"abstract":"Toeplitz CAR flows are a class of E_0-semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non cocycle conjugate E_0-semigroups of type III. We also generalize the type III criterion for Toeplitz CAR flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always either of type I or type III.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2009-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/0023608X-2009-001","citationCount":"9","resultStr":"{\"title\":\"Toeplitz CAR flows and type I factorizations\",\"authors\":\"Masaki Izumi, R. Srinivasan\",\"doi\":\"10.1215/0023608X-2009-001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Toeplitz CAR flows are a class of E_0-semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non cocycle conjugate E_0-semigroups of type III. We also generalize the type III criterion for Toeplitz CAR flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always either of type I or type III.\",\"PeriodicalId\":50142,\"journal\":{\"name\":\"Journal of Mathematics of Kyoto University\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-06-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1215/0023608X-2009-001\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics of Kyoto University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1215/0023608X-2009-001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics of Kyoto University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1215/0023608X-2009-001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 9
摘要
Toeplitz CAR流是一类e_0 -半群，包括R. T. Powers构造的第一个III型例子。我们证明了Toeplitz CAR流包含不可数的互非循环共轭e_0半群。我们还推广了power使用的Toeplitz CAR流的III型准则(后来由W. Arveson改进)，并表明Toeplitz CAR流总是I型或III型。
Toeplitz CAR flows are a class of E_0-semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non cocycle conjugate E_0-semigroups of type III. We also generalize the type III criterion for Toeplitz CAR flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always either of type I or type III.
期刊介绍：
Papers on pure and applied mathematics intended for publication in the Kyoto Journal of Mathematics should be written in English, French, or German. Submission of a paper acknowledges that the paper is original and is not submitted elsewhere.
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