The Krein spectral shift and rank one perturbations of spectra

Details The Krein spectral shift and rank one perturbations of spectra The Krein spectral shift and rank one perturbations of spectra

1996-01-03

arxiv.org/abs/math/9601206v1

Mathematics

Spectral Theory

Scientific paper

We use recent results on the boundary behavior of Cauchy integrals to study the Krein spectral shift of a rank one perturbation problem for self-adjoint operators. As an application, we prove that all self-adjoint rank one perturbations of a self-adjoint operator are pure point if and only if the spectrum of the operator is countable. We also study pairs of pure point operators unitarily equivalent up to a rank one perturbation and give various examples of rank one perturbations of singular spectra.

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