### Numerical radius inequalities for operator matrices

#### 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 ‎$‎A_1, \cdots, A_n‎$‎.‎

#### Article information

Source

Dates
Accepted: 19 June 2018
First available in Project Euclid: 7 July 2018

https://projecteuclid.org/euclid.aot/1530928841

Digital Object Identifier
doi:10.15352/aot.1804-1359

Subjects
Primary: 47A12: Numerical range, numerical radius
Secondary: 47A63‎ ‎47A30

#### Citation

Sahoo, Satyajit; Das, ‎Namita; Mishra, Debasisha. Numerical radius inequalities for operator matrices. Adv. Oper. Theory, advance publication, 7 July 2018. doi:10.15352/aot.1804-1359. https://projecteuclid.org/euclid.aot/1530928841

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