Properties of the spectrum of type π_+ and type π_- of self-adjoint operators in Krein spaces - Trunk, C.; Philipp, F.; Behrndt, J. (Methods of Functional Analysis and Topology, 2006)
We investigate spectral points of type π_+ and type π_- for self-adjoint operators in Krein spaces. In particular a sharp lower bound for the codimension of the linear manifold H_0 occuring in the definition of spectral points of type π_+ and type π_- is determined. Furthermore, we describe the structure of the spectrum in a small neighbourhood of such points and we construct a finite dimensional perturbation which turns a real spectral point of type π_+ (type π_-) into a point of positive (resp. negative) type. As an application we study a singular Sturm-Liouville operator with an indefinite weight.