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Main Title: On Compact Perturbations of Locally Definitizable Selfadjoint Relations in Krein Spaces
Author(s): Behrndt, Jussi
Jonas, Peter
Type: Research Paper
Abstract: The aim of this paper is to prove two perturbation results for a selfadjoint operator A in a Krein space H which can roughly be described as follows: (1) If Δ is an open subset of R, and all spectral subspaces for A corresponding to compact subsets of Δ have finite rank of negativity, the same is true for a selfadjoint operator B in H for which the difference of the resolvents of A and B is compact. (2) The property that there exists some neighbourhood Δ∞ of ∞ such that the restriction of A to a spectral subspace for A corresponding to Δ∞ is a nonnegative operator in H, is preserved under relative Sp perturbations in form sense if the resulting operator is again selfadjoint. The assertion (1) is proved for selfadjoint relations A and B. (1) and (2) generalize some known results.
Subject(s): selfadjoint operators in Krein spaces
compact perturbations
definitizable operators
spectral points of positive and negative type
selfadjoint linear relations
Issue Date: 28-Feb-2003
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 47B50 Operators on spaces with an indefinite metric
47A55 Perturbation theory
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2003, 07
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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