{"title":"Improved Inequalities for Numerical Radius via Cartesian Decomposition","authors":"P. Bhunia, S. Jana, M. S. Moslehian, K. Paul","doi":"10.1134/S0016266323010021","DOIUrl":null,"url":null,"abstract":"<p> We derive various lower bounds for the numerical radius <span>\\(w(A)\\)</span> of a bounded linear operator <span>\\(A\\)</span> defined on a complex Hilbert space, which improve the existing inequality <span>\\(w^2(A)\\geq \\frac{1}{4}\\|A^*A+AA^*\\|\\)</span>. In particular, for <span>\\(r\\geq 1\\)</span>, we show that </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","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/10.1134/S0016266323010021","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
We derive various lower bounds for the numerical radius \(w(A)\) of a bounded linear operator \(A\) defined on a complex Hilbert space, which improve the existing inequality \(w^2(A)\geq \frac{1}{4}\|A^*A+AA^*\|\). In particular, for \(r\geq 1\), we show that
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