Journal of Operator Theory

Volume 58, Issue 2, Fall 2007 pp. 415-440.

Finite Rank Perturbations of Locally Definitizable Self-adjoint Operators in Krein Spaces

Authors: Jussi Behrndt
Author institution: Technische Universitaet Berlin, Institut fuer Mathematik, MA 6-4, Strasse des 17 Juni 136, 10623 Berlin, Germany

Summary: In this paper the well-known result that a definitizable operator in a Krein space remains definitizable after a finite dimensional perturbation is generalized to a class of self-adjoint operators in Krein spaces which locally have the same spectral properties as definitizable operators. As an application the spectral properties of direct sums of indefinite Sturm-Liouville operators are studied.

Keywords: Self-adjoint operators in Krein spaces, finite rank perturbations, (locally) definitizable operators, spectral points of positive and negative type, self-adjoint extensions of symmetric operators, indefinite Sturm-Liouville operators

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