Discrete spectrum in spectral gaps of a self-adjoint operator under unbounded perturbations
type: Item
instance of: scholarly article
title: Discrete spectrum in spectral gaps of a self-adjoint operator under unbounded perturbations
zbMATH Open document ID: 0964.47003
DOI: 10.1007/BF02673743
author: V. A. Sloushch
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-12-11T00:00:00Z
review text: For a self-adjoint operator \(A\) in a Hilbert space \(V\), let \(B\) be its perturbation; \(B= A+ V\), where \(V\) may be unbounded. Let the spectrum of \(A\) contain a gap \((\alpha, \beta)\). The author obtains abstract conditions under which the spectrum of \(B\) is discrete, is finite and does not accumulate to \(\beta\). An estimate for the number of eigenvalues of \(B\) in \((\alpha, \beta)\) is also obtained.
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 1541240
zbMATH Keywords: self-adjoint operator
zbMATH Keywords: perturbation
zbMATH Keywords: spectrum
zbMATH Keywords: number of eigenvalues
reviewed by: P. C. Sinha
MaRDI profile type: Publication
cites work: Q4348376
description: scientific article; zbMATH DE number 1541240