Locally definite operators in indefinite inner product spaces
type: Item
instance of: scholarly article
title: Locally definite operators in indefinite inner product spaces
zbMATH Open document ID: 0879.47017
published in: Mathematische Annalen
publication date: 1997-09-04T00:00:00Z
review text: Let \(A\) be a selfadjoint operator in a Krein space. It is shown that if an interval \(\Delta\) of the real axis consists only of spectral points of positive (or negative) type of \(A\) then \(A\) has a spectral function on \(\Delta\). Another main result states that under a compact selfadjoint perturbation a point of such an interval \(\Delta\) either remains a point of positive (negative, respectively) type or becomes an eigenvalue of finite index of negativity (positivity, respectively). Some of these results remain true for a larger class of indefinite inner product spaces.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 46C20
zbMATH DE Number: 1057246
zbMATH Keywords: definitizable operator
zbMATH Keywords: selfadjoint operator
zbMATH Keywords: Krein space
zbMATH Keywords: spectral points
zbMATH Keywords: spectral function
zbMATH Keywords: compact selfadjoint perturbation
zbMATH Keywords: indefinite inner product spaces
author: Heinz Langer
author: A. Markus
author: Vladimir Matsaev
MaRDI profile type: Publication
full work available at URL: s002080050082
OpenAlex ID: W2073718400
Wikidata QID: Q124629950
DOI: 10.1007/S002080050082
description: scientific article; zbMATH DE number 1057246