Range inclusion and operator equations
type: Item
instance of: scholarly article
title: Range inclusion and operator equations
zbMATH Open document ID: 0868.47014
author: Mohammad Khadivi
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-08-17T00:00:00Z
review text: Let \(A\) and \(D\) be positive operators on a complex Hilbert space \(H\). The operator equation \[ \ell DX+X^*A=A \qquad (\ell>0) \] has a unique solution \(X=C_\ell\) satisfying certain conditions, if there exists a positive operator \(B\) such that \[ AB+ (D-B)A\geq 0. \] The range of \(A\) will be denoted by \(R(A)\). It is proved that the following conjecture is false: If \(R(A+\ell B)\supseteq R(A)\) for all \(\ell\geq 0\), then \(AB+BA\geq 0\).
Mathematics Subject Classification ID: 47A62
Mathematics Subject Classification ID: 47A63
zbMATH DE Number: 902463
reviewed by: Lev A. Sakhnovich
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0043
OpenAlex ID: W1980707221
DOI: 10.1006/JMAA.1996.0043
description: scientific article; zbMATH DE number 902463