Advances in Operator Theory

Numerical radius inequalities for operator matrices

Satyajit Sahoo, ‎Namita Das, and Debasisha Mishra

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‎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

Adv. Oper. Theory, Volume 4, Number 1 (2019), 197-214.

Received: 30 April 2018
Accepted: 19 June 2018
First available in Project Euclid: 7 July 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Aluthge transform ‎‎spectral radius ‎‎numerical radius ‎operator matrix ‎polar decomposition


Sahoo, Satyajit; Das, ‎Namita; Mishra, Debasisha. Numerical radius inequalities for operator matrices. Adv. Oper. Theory 4 (2019), no. 1, 197--214. doi:10.15352/aot.1804-1359.

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