Perturbation theory for self-adjoint operators in Krein spaces

Trunk, Carsten GND

We show that the spectrum of negative type and the spectrum of positive type of self-adjoint operators in Krein spaces are stable under perturbations small in the gap metric. Moreover, we show how these notions can be used to decide whether a given operator has real spectrum only. We apply this to a PT-symmetric multiplication operator.

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Trunk Univ.-Prof. Dr. rer. nat. habil., C., 2007. Perturbation theory for self-adjoint operators in Krein spaces. Preprint /  Technische Universität Ilmenau, Institut für Mathematik, Preprint /  Technische Universität Ilmenau, Institut für Mathematik 07–18.
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