## Numerical radius inequalities for operator matrices.(English)Zbl 06946450

Summary: Several numerical radius inequalities for operator matrices are proved by generalizing earlier inequalities. In particular, the following inequalities are obtained: if $$n$$ is even, $2w(T) \leq \max\{\| A_1 \|, \| A_2 \|,\dots,\| A_n \|\}+\frac{1}{2}\sum_{k=0}^{n-1} \| |A_{n-k}|^{t}|A_{k+1}^{*}|^{1-t} \|,$ and if $$n$$ is odd, $2w(T) \leq \max\{\| A_1 \|,\| A_2 \|,\dots,\| A_n \|\}+w\bigg(\widetilde{A}_{(\frac{n+1}{2})t}\bigg)+ \frac{1}{2}\sum_{k=0}^{n-1} \| |A_{n-k}|^{t}|A_{k+1}^{*}|^{1-t} \|,$ 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 $$A_1, \cdots, A_n$$.

### MSC:

 47A12 Numerical range, numerical radius 47A63 Linear operator inequalities 47A30 Norms (inequalities, more than one norm, etc.) of linear operators
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### References:

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