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Journal of Operator Theory

Volume 64, Issue 2, Fall 2010  pp. 401-416.

Small perturbations of selfadjoint and unitary operators in Krein spaces

Authors:  Tomas Ya. Azizov (1), Peter Jonas (2), and Carsten Trunk (3)
Author institution: (1) Department of Mathematics, Voronezh State University, Universitetskaya pl. 1, 394006 Voronezh, Russia
(2) Technische Universitaet Berlin, Institut fuer Mathematik, MA 6--4, Str. des 17. Juni 136, D-10623 Berlin, Germany
(3) Technische Universitaet Ilmenau, Institut fuer Mathematik, Postfach 10 05 65, D-98684 Ilmenau, Germany

Summary:  We investigate the behaviour of the spectrum of selfadjoint operators in Krein spaces under perturbations with uniformly dissipative operators. Moreover we consider the closely related problem of the perturbation of unitary operators with uniformly bi-expansive. The obtained perturbation results give a new characterization of spectral points of positive type and of type $\pi_{+}$ of selfadjoint (respectively unitary) operators in Krein spaces.

Keywords:  Selfadjoint operators, unitary operators, perturbation by uniformly dissipative operators, Krein spaces, perturbation by uniformly bi-expansive operators

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