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On Finite Rank Perturbations of Selfadjoint Operators in Krein Spaces and Eigenvalues in Spectral Gaps

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Abstract

It is shown that the finiteness of eigenvalues in a spectral gap of a definitizable or locally definitizable selfadjoint operator in a Krein space is preserved under finite rank perturbations. This results is applied to a class of singular Sturm–Liouville operators with an indefinite weight function.

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Acknowledgments

J. Behrndt gratefully acknowledges the stimulating atmosphere at the Isaac Newton Institute for Mathematical Sciences in Cambridge (UK) in July and August 2012 where parts of this paper were written during the research program Spectral Theory of Relativistic Operators.

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Authors and Affiliations

  1. Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 , Graz, Austria

    Jussi Behrndt

  2. Institut für Mathematik, Technische Universität Ilmenau, Postfach 10 05 65, 98684 , Ilmenau, Germany

    Roland Möws & Carsten Trunk

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  1. Jussi Behrndt
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  2. Roland Möws
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Correspondence to Jussi Behrndt.

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Communicated by Aad Dijksma.

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Behrndt, J., Möws, R. & Trunk, C. On Finite Rank Perturbations of Selfadjoint Operators in Krein Spaces and Eigenvalues in Spectral Gaps. Complex Anal. Oper. Theory 8, 925–936 (2014). https://doi.org/10.1007/s11785-013-0318-2

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