{"title":"无不可约Banach表示的阿贝尔拓扑群","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":"{\"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}","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}
Abelian Topological Groups without Irreducible Banach Representations
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.