{"title":"Banach limits: extreme properties, invariance and the Fubini theorem","authors":"N. Avdeev, E. Semenov, A. Usachev","doi":"10.1090/spmj/1717","DOIUrl":null,"url":null,"abstract":"A Banach limit on the space of all bounded real sequences is a positive normalized linear functional that is invariant with respect to the shift. The paper studies such properties of Banach limits as multiplicativity and the validity of Fubini’s theorem. A subset of Banach limits invariant with respect to dilation operators is also treated.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1717","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
A Banach limit on the space of all bounded real sequences is a positive normalized linear functional that is invariant with respect to the shift. The paper studies such properties of Banach limits as multiplicativity and the validity of Fubini’s theorem. A subset of Banach limits invariant with respect to dilation operators is also treated.
期刊介绍：
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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