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

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