On convergence of inverse functions of operators
type: Item
instance of: scholarly article
title: On convergence of inverse functions of operators
zbMATH Open document ID: 0671.47015
DOI: 10.1016/0022-1236(88)90103-6
author: Arthur Jaffe
author: Andrzej Leśniewski
author: Konrad Osterwalder
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: Let \(\{A_ n\}^{\infty}_{n=1}\) be a sequence of selfadjoint operators on a Hilbert space and let F be a real-valued function. The problem is whether the convergence of the sequence \(\{F(A_ n)\}\) ensures the convergence of \(\{A_ n\}\) to a selfadjoint limit. The authors give sufficient conditions imposed on a function f and on the sequence \(\{A_ n\}\) under which the existence of a norm-resolvent limit of \(\{F(A_ n\}\), \(F(A_ n)=^{def}f(| A_ n|)\), implies the existence of a selfadjoint operator A which is a norm-resolvent limit of \(\{A_ n\}\).
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 4098082
zbMATH Keywords: selfadjoint operators
zbMATH Keywords: norm-resolvent limit
reviewed by: Teresa Regińska
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90103-6
OpenAlex ID: W2072266841
cites work: Singular perturbations of selfadjoint operators
cites work: The two-dimensional, \(N=2\) Wess-Zumino model on a cylinder
cites work: Q3909512
description: scientific article; zbMATH DE number 4098082