• Corpus ID: 119039501

The Krein spectral shift and rank one perturbations of spectra

  title={The Krein spectral shift and rank one perturbations of spectra},
  author={Alexei Poltoratski},
  journal={arXiv: Spectral Theory},
  • A. Poltoratski
  • Published 3 January 1996
  • Mathematics
  • arXiv: Spectral Theory
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… 
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