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, Jussi / Leben, Leslie / Martínez Pería, Francisco / et al: Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces. 2013.

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