{"title":"Composition operators in $bv_p$-spaces, part I: acting conditions and boundedness","authors":"Daria Bugajewska, Piotr Kasprzak","doi":"arxiv-2407.14176","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to give the answer to the problem of\ncharacterization of acting conditions (necessary as well as sufficient) for\ncomposition operators in some sequence spaces. We also characterize their\nboundedness and local boundedness. We focus on composition operators acting to\nor from the space $bv_p(E)$ of all sequences of $p$-bounded variation; here\n$p\\geq 1$ and $E$ is a normed space.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.14176","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to give the answer to the problem of
characterization of acting conditions (necessary as well as sufficient) for
composition operators in some sequence spaces. We also characterize their
boundedness and local boundedness. We focus on composition operators acting to
or from the space $bv_p(E)$ of all sequences of $p$-bounded variation; here
$p\geq 1$ and $E$ is a normed space.
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