Abstract
Several numerical radius inequalities for operator matrices are proved by generalizing earlier inequalities. In particular, the following inequalities are obtained: if $n$ is even, \[2w(T) \leq \max\{\| A_1 \|, \| A_2 \|,\ldots, \| A_n \|\}+\frac{1}{2}\displaystyle\sum_{k=0}^{n-1} \|~ |A_{n-k}|^{t}|A_{k+1}^{*}|^{1-t} \|,\] and if $n$ is odd, \[2w(T) \leq \max\{\| A_1 \|,\| A_2 \|,\ldots,\| A_n \|\}+ w\bigg(\widetilde{A}_{(\frac{n+1}{2})t}\bigg)+ \frac{1}{2}\displaystyle\sum_{k=0}^{n-1} \|~ |A_{n-k}|^{t}|A_{k+1}^{*}|^{1-t} \|,\] for all $t\in [0, 1]$, $ A_i$'s are bounded linear operators on the Hilbert space $\mathcal{H}$, and $T$ is off diagonal matrix with entries $A_1, \cdots, A_n$.
Citation
Satyajit Sahoo. Namita Das. Debasisha Mishra. "Numerical radius inequalities for operator matrices." Adv. Oper. Theory 4 (1) 197 - 214, Winter 2019. https://doi.org/10.15352/aot.1804-1359
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