Preprint 03-2003

On Locally Definite Operators in Krein Spaces

Author(s) : Peter Jonas

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 03-2003

MSC 2000

47B50 Operators on spaces with an indefinite metric

47A56 Functions whose values are linear operators

47A60 Functional calculus

Abstract :
For selfadjoint operators in Krein spaces the notions of spectral points of positive and negative type are basic in the spectral and perturbation theory of these operators. The aim of this paper is to give different characterizations of these sign types of spectral points. Moreover a local variant of definitizability is characterized in various ways.

Keywords : selfadjoint and unitary operators in Krein spaces, spectral points of positive and negative type, spectral function, definitizable operators, selfadjoint linear relations