{"title":"Representation and normality of \\(*\\)-paranormal absolutely norm attaining operators","authors":"Neeru Bala","doi":"10.1007/s44146-023-00063-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, we give a representation of absolutely norm attaining <span>\\(*\\)</span>-paranormal operators. More specifically, we prove that every <span>\\(*\\)</span>-paranormal absolutely norm attaining operator <i>T</i> can be decomposed as <span>\\(U\\oplus D\\)</span>, where <i>U</i> is a direct sum of scalar multiples of unitary operators and <i>D</i> is an upper triangular block operator matrix. Later, we provide a sufficient condition under which a <span>\\(*\\)</span>-paranormal absolutely norm attaining operator is normal.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 1-2","pages":"167 - 181"},"PeriodicalIF":0.5000,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-023-00063-0.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACTA SCIENTIARUM MATHEMATICARUM","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s44146-023-00063-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this article, we give a representation of absolutely norm attaining \(*\)-paranormal operators. More specifically, we prove that every \(*\)-paranormal absolutely norm attaining operator T can be decomposed as \(U\oplus D\), where U is a direct sum of scalar multiples of unitary operators and D is an upper triangular block operator matrix. Later, we provide a sufficient condition under which a \(*\)-paranormal absolutely norm attaining operator is normal.
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