利用笛卡尔分解改进的数值半径不等式

Pub Date : 2023-09-05 DOI:10.1134/S0016266323010021
P. Bhunia, S. Jana, M. S. Moslehian, K. Paul
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引用次数: 0

摘要

我们导出了复Hilbert空间上定义的有界线性算子\(A\)的数值半径\(w(A)\)的各种下界,改进了现有不等式\(w^2(A)\geq \frac{1}{4}\|A^*A+AA^*\|\)。特别地,对于\(r\geq 1\),我们展示了
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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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