Analysis Mathematica, Volume (45), No (4), Year (2019-12) , Pages (687-703)

Title : ( Sharp Inequalities for the Numerical Radii of Block Operator Matrices )

Authors: M. Ghaderi Aghideh , Mohammad Sal Moslehian , Jamal Rooin ,

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Abstract

‎In this paper‎, ‎we present several sharp upper bounds for the numerical radii of the diagonal and off-diagonal parts of‎ ‎the $ 2 \\\\times 2$ block operator matrix‎ ‎$ \\\\begin{bmatrix}‎ ‎A& B \\\\\\\\‎ ‎C& D \\\\end{bmatrix} $‎. ‎Among extensions of some results of Kittaneh et al.‎, ‎it is shown that if‎ ‎$ T= \\\\begin{bmatrix}‎ ‎A& 0 \\\\\\\\‎ ‎0& D \\\\end{bmatrix}$‎, ‎and $f$ and $g$ are non-negative continuous functions on $ [0‎, ‎\\\\infty ) $ such that $ f(t)g(t)=t \\\\ (t \\\\geq 0) $‎, ‎then for all non-negative nondecreasing convex functions $h$ on‎ ‎$ [0‎, ‎\\\\infty ) $‎, ‎we obtain that‎ ‎\\\\begin{align*}‎ ‎& h\\\\left( w^r(T)\\\\right) \\\\\\\\‎ ‎& \\\\leq \\\\max \\\\left(‎ ‎\\\\left\\\\| \\\\frac{1}{p} h\\\\left(f^{pr}(\\\\left| A \\\\right| )\\\\right)‎+ ‎\\\\frac{1}{q}h\\\\left(g^{qr}(\\\\left| A^* \\\\right| )\\\\right)\\\\right\\\\|‎ ,‎\\\\left\\\\|\\\\frac{1}{p} h\\\\left( f^{pr}(\\\\left| D \\\\right| )\\\\right)‎+ ‎\\\\frac{1}{q}h\\\\left(g^{qr}(\\\\left| D^* \\\\right| )\\\\right)\\\\right\\\\|\\\\right)‎, ‎\\\\end{align*}‎ ‎where $ p‎, ‎q > 1 $ with‎ ‎$\\\\frac{1}{p}‎ + ‎\\\\frac{1}{q} =1$‎, ‎and $ r \\\\min (p‎, ‎q )\\\\geq 2 $‎.

Keywords

, Numerical radius; convexity; mixed Cauchy, , Schwarz inequality; polar decomposition
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@article{paperid:1077828,
author = {M. Ghaderi Aghideh and Sal Moslehian, Mohammad and جمال رویین},
title = {Sharp Inequalities for the Numerical Radii of Block Operator Matrices},
journal = {Analysis Mathematica},
year = {2019},
volume = {45},
number = {4},
month = {December},
issn = {0133-3852},
pages = {687--703},
numpages = {16},
keywords = {Numerical radius; convexity; mixed Cauchy--Schwarz inequality; polar decomposition},
}

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%0 Journal Article
%T Sharp Inequalities for the Numerical Radii of Block Operator Matrices
%A M. Ghaderi Aghideh
%A Sal Moslehian, Mohammad
%A جمال رویین
%J Analysis Mathematica
%@ 0133-3852
%D 2019

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