On a class of selfadjoint operators in Krein space and their compact perturbations
type: Item
instance of: scholarly article
title: On a class of selfadjoint operators in Krein space and their compact perturbations
zbMATH Open document ID: 0651.47020
DOI: 10.1007/BF01202078
author: Peter Jonas
published in: Integral Equations and Operator Theory
publication date: 1988-01-01T00:00:00Z
review text: The objectives are linear operators, selfadjoint with respect to the indefinite inner product of a Krein space. A selfadjoint operator is called definitizable if a certain real polynomial of it is non-negative. For a definitizable operator \textit{H. Langer} [Spektralfunktionen einer Klasse J-selfadjungierter Operatoren, Math. Nachr. 33, 107-120 (1967; Zbl 0147.121)] constructed a spectral function and established stability under a Macaev class perturbation. In the present paper the author extends these results to a wider class of selfadjoint operators, containing definitizable operators. Here definitizability is replaced by a growth condition of resolvents near the real axis and normality of the spectrum off the real axis.
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 4061978
zbMATH Keywords: J-selfadjoint operator
zbMATH Keywords: indefinite inner product
zbMATH Keywords: Krein space
zbMATH Keywords: definitizable operator
zbMATH Keywords: spectral function
zbMATH Keywords: Macaev class perturbation
zbMATH Keywords: growth condition of resolvents near the real axis
zbMATH Keywords: normality of the spectrum off the real axis
reviewed by: T. Ando
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4061978