{"title":"Unbounded strictly singular operators","authors":"R.W. Cross","doi":"10.1016/S1385-7258(88)80004-0","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>D(T)⊂X→Y</em> be an unbounded linear operator where <em>X</em> and <em>Y</em> are normed spaces. It is shown that if <em>Y</em> is complete then <em>T</em> is strictly singular if and only if <em>T</em> is the sum of a continuous strictly singular operator and an unbounded finite rank operator. A counterexample is constructed for the case in which <em>Y</em> is not complete.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 245-248"},"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)80004-0","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725888800040","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
Let D(T)⊂X→Y be an unbounded linear operator where X and Y are normed spaces. It is shown that if Y is complete then T is strictly singular if and only if T is the sum of a continuous strictly singular operator and an unbounded finite rank operator. A counterexample is constructed for the case in which Y is not complete.
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