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

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