Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces

Behrndt, Jussi GND; Leben, Leslie; Martínez Pería, Francisco; Möws, Roland GND; Trunk, Carsten GND

Let A and B be selfadjoint operators in a Krein space and assume that the resolvent difference of A and B is of rank one. In the case that A is nonnegative and I is an open interval such that the spectrum of A in I consists of isolated eigenvalues we prove sharp estimates on the numbers and multiplicities of eigenvalues of B in I. The general result is illustrated with eigenvalue estimates for singular left definite Sturm-Liouville differential operators.

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Behrndt Univ.-Prof. Dr., J., Leben, L., Martínez Pería Prof. Dr., F., Möws Dr. rer. nat., R., Trunk Univ.-Prof. Dr. rer. nat. habil., C., 2013. Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces. Preprint /  Technische Universität Ilmenau, Institut für Mathematik, Preprint /  Technische Universität Ilmenau, Institut für Mathematik 13–13.
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