{"title":"A Koopman-von Neumann type theorem on the convergence of Cesàro means in Riesz spaces","authors":"Jonathan Homann, Wen-Chi Kuo, B. Watson","doi":"10.1090/BPROC/75","DOIUrl":null,"url":null,"abstract":"We extend the Koopman-von Neumann convergence condition on the Cesàro mean to the context of a Dedekind complete Riesz space with weak order unit. As a consequence, a characterisation of conditional weak mixing is given in the Riesz space setting. The results are applied to convergence in \n\n \n \n L\n 1\n \n L^1\n \n\n.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"98 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/BPROC/75","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We extend the Koopman-von Neumann convergence condition on the Cesàro mean to the context of a Dedekind complete Riesz space with weak order unit. As a consequence, a characterisation of conditional weak mixing is given in the Riesz space setting. The results are applied to convergence in
L
1
L^1
.
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