Spectral points of definite type and type π for linear operators and relations in Krein spaces

Spectral points of positive and negative type, and type π+ and type π− for closed linear operators and relations in Krein spaces are introduced with the help of approximative eigensequences. The main objective of the paper is to study these sign type properties in the non-selfadjoint case under various kinds of perturbations, e.g. compact perturbations and perturbations small in the gap metric. Many of the obtained perturbation results are also new for the special case of bounded and unbounded selfadjoint operators in Krein spaces.