{"title":"III型因子中的奇异MASAs和Connes的双中心化性质","authors":"Cyril Houdayer, S. Popa","doi":"10.2969/ASPM/08010109","DOIUrl":null,"url":null,"abstract":"We show that any type ${\\rm III_1}$ factor with separable predual satisfying Connes' Bicentralizer Property (CBP) has a singular maximal abelian $\\ast$-subalgebra that is the range of a normal conditional expectation. We also investigate stability properties of CBP under finite index extensions/restrictions of type ${\\rm III_1}$ factors.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Singular MASAs in type III factors and Connes' Bicentralizer Property\",\"authors\":\"Cyril Houdayer, S. Popa\",\"doi\":\"10.2969/ASPM/08010109\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that any type ${\\\\rm III_1}$ factor with separable predual satisfying Connes' Bicentralizer Property (CBP) has a singular maximal abelian $\\\\ast$-subalgebra that is the range of a normal conditional expectation. We also investigate stability properties of CBP under finite index extensions/restrictions of type ${\\\\rm III_1}$ factors.\",\"PeriodicalId\":351745,\"journal\":{\"name\":\"arXiv: Operator Algebras\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-04-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2969/ASPM/08010109\",\"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: Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2969/ASPM/08010109","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Singular MASAs in type III factors and Connes' Bicentralizer Property
We show that any type ${\rm III_1}$ factor with separable predual satisfying Connes' Bicentralizer Property (CBP) has a singular maximal abelian $\ast$-subalgebra that is the range of a normal conditional expectation. We also investigate stability properties of CBP under finite index extensions/restrictions of type ${\rm III_1}$ factors.
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