Variation of Discrete Spectra for Non-Selfadjoint Perturbations of Selfadjoint Operators |
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Authors: | Marcel Hansmann |
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Institution: | 1. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
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Abstract: | Let B = A + K where A is a bounded selfadjoint operator and K is an element of the von Neumann–Schatten ideal ${\mathcal{S}_{p}}$ with p > 1. Let {λ n } denote an enumeration of the discrete spectrum of B. We show that ${\sum_n {\rm dist}(\lambda_n, \sigma(A))^p}$ is bounded from above by a constant multiple of ${\|K\|_{p}^p}$ . We also derive a unitary analog of this estimate and apply it to obtain new estimates on zero-sets of Cauchy transforms. |
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