{"title":"Characterizations of Carleman operators","authors":"Dan Tudor Vuza","doi":"10.1016/S1385-7258(89)80009-5","DOIUrl":null,"url":null,"abstract":"<div><p>We prove an improved version of Korotkov's characterization of Carleman operators and we determine those bounded linear operators <em>U: L<sub>ϱ</sub>(μ)→L<sub>2</sub>(ν) (L<sub>ϱ</sub>(μ)</em> being a Banach function space) with the property that for every bounded linear operator <em>B</em> on <em>L<sub>2</sub>(ν)</em>, the restriction of <em>BU</em> to a given order ideal <em>E</em> in <em>L<sub>ϱ</sub>(μ)</em> is integral or regular as an operator from <em>E</em> to <em>L<sub>0</sub>(ν)</em>.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 3","pages":"Pages 343-354"},"PeriodicalIF":0.0000,"publicationDate":"1989-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80009-5","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725889800095","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We prove an improved version of Korotkov's characterization of Carleman operators and we determine those bounded linear operators U: Lϱ(μ)→L2(ν) (Lϱ(μ) being a Banach function space) with the property that for every bounded linear operator B on L2(ν), the restriction of BU to a given order ideal E in Lϱ(μ) is integral or regular as an operator from E to L0(ν).
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