{"title":"A characterization of dual Banach lattices","authors":"V. Caselles","doi":"10.1016/S1385-7258(89)80015-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we give a characterization of dual Banach lattices. In fact, we prove that a Banach function space <em>E</em> on a separable measure space which has the Fatou property is a dual Banach lattice if and only if all positive operators from <em>L</em><sup>1</sup>(0,1) into <em>E</em> are abstract kernel operators, hence extending the fact, proved by M. Talagrand, that separable Banach lattices with the Radon-Nikodym property are dual Banach lattices.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 1","pages":"Pages 35-47"},"PeriodicalIF":0.0000,"publicationDate":"1989-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80015-0","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725889800150","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper we give a characterization of dual Banach lattices. In fact, we prove that a Banach function space E on a separable measure space which has the Fatou property is a dual Banach lattice if and only if all positive operators from L1(0,1) into E are abstract kernel operators, hence extending the fact, proved by M. Talagrand, that separable Banach lattices with the Radon-Nikodym property are dual Banach lattices.
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