{"title":"On the Commutativity of Closed Symmetric Operators","authors":"S. Dehimi, M. H. Mortad, A. Bachir","doi":"10.1007/s10476-023-0226-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we mainly show that if a product <i>AB</i> (or <i>BA</i>) of a closed symmetric operator <i>A</i> and a bounded positive operator <i>B</i> is normal, then it is self-adjoint. Equivalently, this means that <i>B</i> commutes with <i>A</i>. Certain generalizations and consequences are also presented.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0226-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we mainly show that if a product AB (or BA) of a closed symmetric operator A and a bounded positive operator B is normal, then it is self-adjoint. Equivalently, this means that B commutes with A. Certain generalizations and consequences are also presented.
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