{"title":"利用笛卡尔分解改进的数值半径不等式","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":"{\"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}","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}
Improved Inequalities for Numerical Radius via Cartesian Decomposition
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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