{"title":"von Neumann代数的Banach-Mazur稳定性","authors":"J. Roydor","doi":"10.1142/s1793525321500151","DOIUrl":null,"url":null,"abstract":"We initiate the study of perturbation of von Neumann algebras relatively to the Banach–Mazur distance. We first prove that the type decomposition is continuous, i.e. if two von Neumann algebras are close, then their respective summands of each type are close. We then prove that, under some vanishing conditions on its Hochschild cohomology groups, a von Neumann algebra is Banach–Mazur stable, i.e. any von Neumann algebra which is close enough is actually Jordan ∗-isomorphic. These vanishing conditions are possibly empty.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Banach–Mazur stability of von Neumann algebras\",\"authors\":\"J. Roydor\",\"doi\":\"10.1142/s1793525321500151\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We initiate the study of perturbation of von Neumann algebras relatively to the Banach–Mazur distance. We first prove that the type decomposition is continuous, i.e. if two von Neumann algebras are close, then their respective summands of each type are close. We then prove that, under some vanishing conditions on its Hochschild cohomology groups, a von Neumann algebra is Banach–Mazur stable, i.e. any von Neumann algebra which is close enough is actually Jordan ∗-isomorphic. These vanishing conditions are possibly empty.\",\"PeriodicalId\":49151,\"journal\":{\"name\":\"Journal of Topology and Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Topology and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793525321500151\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793525321500151","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We initiate the study of perturbation of von Neumann algebras relatively to the Banach–Mazur distance. We first prove that the type decomposition is continuous, i.e. if two von Neumann algebras are close, then their respective summands of each type are close. We then prove that, under some vanishing conditions on its Hochschild cohomology groups, a von Neumann algebra is Banach–Mazur stable, i.e. any von Neumann algebra which is close enough is actually Jordan ∗-isomorphic. These vanishing conditions are possibly empty.
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This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.
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