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

Via approximative eigensequences we introduce the notion of spectral points of type π+ and π- for self-adjoint operators in Krein spaces. They are stable under compact perturbations. For real spectral points of type π+ and π- 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 π+ or type π- are Pontryagin spaces.