{"title":"Linear Interpolation and the Elementary Operators on ()","authors":"H. Jin-chuan","doi":"10.1360/YA1993-36-9-1025","DOIUrl":null,"url":null,"abstract":"Let be a Banach space.In this paper the sufficient and necessary condi- tions for an elementary operator on () to be of finite rank or of rank one are obtained; a characterization of an abstract linear mapping on () to be a finite-rank elementary operator is given;and it is also shown that a linear interpolation of finitely many elemen- tary operators △ 1 ,…,△ k is still an elementary operator though it may not be a linear combi- nation of △ i 's.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"53 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1360/YA1993-36-9-1025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
Let be a Banach space.In this paper the sufficient and necessary condi- tions for an elementary operator on () to be of finite rank or of rank one are obtained; a characterization of an abstract linear mapping on () to be a finite-rank elementary operator is given;and it is also shown that a linear interpolation of finitely many elemen- tary operators △ 1 ,…,△ k is still an elementary operator though it may not be a linear combi- nation of △ i 's.
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