Translator Disclaimer
Winter 2019 Numerical radius inequalities for operator matrices
Satyajit Sahoo, ‎Namita Das, Debasisha Mishra
Adv. Oper. Theory 4(1): 197-214 (Winter 2019). DOI: 10.15352/aot.1804-1359

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

Download 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

Information

Received: 30 April 2018; Accepted: 19 June 2018; Published: Winter 2019
First available in Project Euclid: 7 July 2018

zbMATH: 06946450
MathSciNet: MR3867341
Digital Object Identifier: 10.15352/aot.1804-1359

Subjects:
Primary: 47A12
Secondary: 47A30, 47A63

Rights: Copyright © 2019 Tusi Mathematical Research Group

JOURNAL ARTICLE
18 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.4 • No. 1 • Winter 2019
Back to Top