On some perturbation inequalities for operators
type: Item
instance of: scholarly article
title: On some perturbation inequalities for operators
zbMATH Open document ID: 0659.47016
DOI: 10.1016/0024-3795(88)90034-1
author: Rajendra Bhatia
author: Fuad Kittaneh
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Let E, F be any two Hilbert spaces, and let L(E,F) denote the space of bounded linear operators from E to F. Let L(E,E) be denoted simply as L(E). It has long been known [see \textit{M. Rosenblum}, Duke Math. J. 23, 263-269 (1956; Zbl 0073.330)] that if A and B are elements of L(E) and L(F), respectively, such that spectrum of A and spectrum of B are disjoint, then for every S in L(F,E) the equation \(AX-XB=S\) has a unique solution X in L(F,E). An estimate for the norm of the solution obtained by \textit{R. Bhatia}, \textit{C. Davis} and \textit{A. McIntosh} for normal operators A and B [Linear Algebra Appl. 52-53, 45-67 (1983; Zbl 0518.47013)] is shown to be valid for a larger class (for subnormal operators). Recall that an operator A in L(E) is subnormal if it has a normal extension; i.e., there exist a Hilbert space K containing H as a subspace and a normal operator M in L(K) which leaves H invariant and which coincides with A when restricted to H.
reviewed by: S.D.Karakozov
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47A62
zbMATH DE Number: 4078063
zbMATH Keywords: subnormal operators
zbMATH Keywords: normal extension
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90034-1
OpenAlex ID: W1969331069
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description: scientific article; zbMATH DE number 4078063