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arXiv · 1802.10243

Absolute continuity of spectral shift

Mark Malamud·Hagen Neidhardt·Vladimir Peller
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Abstract

In this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish the absolute continuity of spectral shift, we use the Sz.-Nagy theorem on the absolute continuity of the spectrum of the minimal unitary dilation of a completely nonunitary contraction. We also give a construction of an intermediate contraction for a pair of contractions with trace class difference.

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Mark Malamud, Hagen Neidhardt, Vladimir Peller. 2018-02-28. Absolute continuity of spectral shift. https://arxiv.org/abs/1802.10243

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