Spectral points of type + and − of self-adjoint operators in Krein spaces

Via approximative eigensequences we introduce the notion of spectral points of type + and − for self-adjoint operators in Krein spaces. They are stable under compact perturbations. For real spectral points of type + and − which are not in the interior of the spectrum we prove that the growth of the resolvent in some neighbourhood of them is of finite order. There exists a local spectral function with singularities. It turns out that all spectral subspaces corresponding to sufficiently small neighbourhoods of points of type + or type − are Pontryagin spaces. © 2005 Elsevier Inc. All rights reserved