On \(\mathbb{A}\)-numerical radius equalities and inequalities for certain operator matrices
type: Item
instance of: scholarly article
title: On \(\mathbb{A}\)-numerical radius equalities and inequalities for certain operator matrices
author: Fuad Kittaneh
author: Satyajit Sahoo
published in: Annals of Functional Analysis
publication date: 2021-07-30T00:00:00Z
review text: Let \(H\) be a Hilbert space, \(A\) a positive bounded operator on \(H\), and let \(\mathbb A\) be the diagonal \(n{\times}n\) matrix with diagonal entries equal to \(A\). Then \(\mathbb A\) determines a semidefinite inner product on \(H^n\) by \(\langle x,y\rangle_\mathbb A=\langle \mathbb Ax,y\rangle\), \(x,y\in H^n\). Given a bounded operator \(T\) on \(H^n\), the \(\mathbb A\)-numerical radius is defined by \(w_\mathbb A(T)=\sup\{|\langle Tx,x\rangle_\mathbb A|:x\in H^n,\|x\|_\mathbb A\leq 1\}\). The authors prove some equalities and inequalities for the \(\mathbb A\)-numerical radius for circular and tri-diagonal matrices with entries being bounded operators on \(H\).
Mathematics Subject Classification ID: 47A12
Mathematics Subject Classification ID: 47B36
zbMATH DE Number: 7376590
zbMATH Keywords: \(\mathbb{A}\)-numerical radius
zbMATH Keywords: positive operator
zbMATH Keywords: semi-inner product
zbMATH Keywords: inequality
zbMATH Keywords: circulant operator matrix
zbMATH Keywords: tridiagonal operator matrix
reviewed by: Vladimir M. Manuilov
MaRDI profile type: Publication
full work available at URL: s43034-021-00137-6
OpenAlex ID: W3192478114
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DOI: 10.1007/S43034-021-00137-6
description: scientific article; zbMATH DE number 7376590