{"title":"Isolation amongst composition operators on $L^p(\\mu)$-spaces $(1\\le p \\le \\infty)$","authors":"Ashish Naudiyal, H. Chandra","doi":"10.7153/oam-2023-17-13","DOIUrl":null,"url":null,"abstract":". In this paper we show that each composition operator is isolated in comp ( L p ) ( 1 (cid:2) p (cid:2) ∞ ) under the norm topology. We also prove that while each composition operator is non-isolated in comp ( (cid:2) p ) ( 1 (cid:2) p < ∞ ) under the strong operator topology, every composition operator is isolated in comp ( L ∞ ) under the strong operator topology.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/oam-2023-17-13","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
. In this paper we show that each composition operator is isolated in comp ( L p ) ( 1 (cid:2) p (cid:2) ∞ ) under the norm topology. We also prove that while each composition operator is non-isolated in comp ( (cid:2) p ) ( 1 (cid:2) p < ∞ ) under the strong operator topology, every composition operator is isolated in comp ( L ∞ ) under the strong operator topology.
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