Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators

Abstract

Let B=A+K where A is a bounded selfadjoint operator and K is an element of the von Neumann-Schatten ideal S_p with p>1. Let {λ_n} denote an enumeration of the discrete spectrum of B. We show that $\sum_n \dist(λ_n, σ(A))^p$ is bounded from above by a constant multiple of |K|_p^p. We also derive a unitary analog of this estimate and apply it to obtain new estimates on zero-sets of Cauchy transforms.

Differences to previous version: Extended Introduction, new Section 5, additional references. To appear in Int. Eq. Op. Theory

References in corpus (1)

• Blaschke-type conditions in unbounded domains, generalized convexity and applications in perturbation theory

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