{"title":"Abelian Topological Groups without Irreducible Banach Representations","authors":"V. Pestov","doi":"10.1201/9780429187605-29","DOIUrl":null,"url":null,"abstract":"We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable Hilbert space.","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"abelian groups, module theory, and topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/9780429187605-29","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable Hilbert space.
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