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Journal of Operator Theory

Volume 71, Issue 1, Winter 2014  pp. 157-173.

Variation of discrete spectra of non-negative operators in Krein spaces

Authors: Jussi Behrndt (1), Leslie Leben (2), and Friedrich Philipp (3)
Author institution: (1) Institut fuer Numerische Mathematik, Technische Universitaet Graz, 8010 Graz, Austria
(2) Institut fuer Mathematik, Technische Universitaet Ilmenau, 98684 Ilmenau, Germany
(3) Institut fuer Mathematik, Technische Universitaet Berlin, 10623 Berlin, Germany

Summary:  We study the variation of the discrete spectrum of a bounded non-negative operator in a Krein space under a non-negative Schatten class perturbation of order $p$. It turns out that there exist so-called extended enumerations of discrete eigenvalues of the unperturbed and perturbed operator, respectively, whose difference is an $\ell^p$-sequence. This result is a Krein space version of a theorem by T. Kato for selfadjoint operators in Hilbert spaces.

Keywords:  Krein space, discrete spectrum, analytic perturbation theory, Schatten-von Neumann ideal

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