{"title":"一类与局部紧群相关的Banach代数的Arens正则性及相关问题的统一研究","authors":"Anthony to-Ming Lau;Ali Ülger","doi":"10.1093/qmath/haab005","DOIUrl":null,"url":null,"abstract":"Based on Katznelson–Tzafriri Theorem on power bounded operators, we prove in this paper a theorem, which applies to the most of the classical Banach algebras of harmonic analysis associated with locally compact groups, to deal with the problems when a given Banach algebra A is Arens regular and when A is an ideal in its bidual. In the second part of the paper, we study the topological center of the bidual of a class of Banach algebras with a multiplier bounded approximate identity.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":"72 4","pages":"1311-1327"},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haab005","citationCount":"0","resultStr":"{\"title\":\"A Unified Approach to the Arens Regularity and Related Problems for a Class of Banach Algebras Associated with Locally Compact Groups\",\"authors\":\"Anthony to-Ming Lau;Ali Ülger\",\"doi\":\"10.1093/qmath/haab005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Based on Katznelson–Tzafriri Theorem on power bounded operators, we prove in this paper a theorem, which applies to the most of the classical Banach algebras of harmonic analysis associated with locally compact groups, to deal with the problems when a given Banach algebra A is Arens regular and when A is an ideal in its bidual. In the second part of the paper, we study the topological center of the bidual of a class of Banach algebras with a multiplier bounded approximate identity.\",\"PeriodicalId\":54522,\"journal\":{\"name\":\"Quarterly Journal of Mathematics\",\"volume\":\"72 4\",\"pages\":\"1311-1327\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1093/qmath/haab005\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quarterly Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/9690908/\",\"RegionNum\":4,\"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":"Quarterly Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://ieeexplore.ieee.org/document/9690908/","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Unified Approach to the Arens Regularity and Related Problems for a Class of Banach Algebras Associated with Locally Compact Groups
Based on Katznelson–Tzafriri Theorem on power bounded operators, we prove in this paper a theorem, which applies to the most of the classical Banach algebras of harmonic analysis associated with locally compact groups, to deal with the problems when a given Banach algebra A is Arens regular and when A is an ideal in its bidual. In the second part of the paper, we study the topological center of the bidual of a class of Banach algebras with a multiplier bounded approximate identity.
期刊介绍:
The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.