Bounds on perturbations of self-adjoint operators
type: Item
instance of: scholarly article
title: Bounds on perturbations of self-adjoint operators
zbMATH Open document ID: 0870.47011
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-09-30T00:00:00Z
review text: Suppose the spectrum of the selfadjoint operator \(T^0\) is known while the spectrum of the perturbed selfadjoint operator \(T=T^0+V\) is unknown. If \(V\) is a bounded operator, the spectrum of \(T\) is expected to be shifted from that of \(T^0\) by no more than the norm \(|V|\) of \(V\). It is pointed out by \textit{M. M. Skriganov} [Proc. Steklov Inst. Math. 171 (1987; Zbl 0615.47004)] that in certain situations the size of this shift is much less than \(|V|\). The paper under review improves it to give some tighter bounds on this shift. The result is also compared with those to be obtained by using Temple's inequality and the generalized Temple's inequality and some applications are given.
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 930182
zbMATH Keywords: spectrum
zbMATH Keywords: perturbed selfadjoint operator
zbMATH Keywords: generalized Temple's inequality
author: E. L. Green
reviewed by: Takashi Ichinose
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0274
OpenAlex ID: W2037496277
DOI: 10.1006/JMAA.1996.0274
description: scientific article; zbMATH DE number 930182