{"title":"On the space of all regular operators from C(K) into C(K)","authors":"A. Andreu, J.M. Mazón, S. Segura de Léon","doi":"10.1016/S1385-7258(88)80001-5","DOIUrl":null,"url":null,"abstract":"<div><p>It is known that <em>L<sup>r</sup>(E, C(K))</em>, the space of all regular operators from <em>E</em> into <em>C(K)</em>, is a Riesz space for all Riesz spaces <em>E</em> if and only if <em>K</em> is Stonian. We prove that this statement holds if <em>E</em> is replaced by <em>C(K)</em>, where <em>K</em> is a compact space, the cardinal number of which satisfies a certain condition.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 225-230"},"PeriodicalIF":0.0000,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80001-5","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725888800015","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
It is known that Lr(E, C(K)), the space of all regular operators from E into C(K), is a Riesz space for all Riesz spaces E if and only if K is Stonian. We prove that this statement holds if E is replaced by C(K), where K is a compact space, the cardinal number of which satisfies a certain condition.
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