Absolute continuity of spectral shift

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 spectral measure 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. © 2018

Authors
Malamud M.M. 1 , Neidhardt H.2 , Peller V.V. 1, 3
Journal
Journal of Functional Analysis
Publisher
Academic Press Inc.
Language
English
Status
Published
Link
External link
DOI
10.1016/j.jfa.2018.05.011
Year
2018
Organizations
  • 1 People's Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 6117198, Russian Federation
  • 2 Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, Berlin, D-10117, Germany
  • 3 Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States
Keywords
Contractions; Dissipative operators; Lifshits–Krein trace formula; Self-adjoint operators; Spectral shift function; Unitary operators
Date of creation
19.10.2018
Date of change
04.03.2021
Short link
https://repository.rudn.ru/en/records/article/record/7217/
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