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Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions

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Functional Analysis and Its Applications Aims and scope

Abstract

In this paper we prove that for an arbitrary pair {T 1, T 0} of contractions on Hilbert space with trace class difference, there exists a function ξ in L 1(T) (called a spectral shift function for the pair {T 1, T 0}) such that the trace formula trace(f(T 1) − f(T 0)) = ∫T f′(ζ)ξ(ζ)dζ holds for an arbitrary operator Lipschitz function f analytic in the unit disk.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics NAS of Ukraine, Donetsk, Ukraine

    M. M. Malamud

  2. People’s Friendship University of Russia (RUDN University), Moscow, Russia

    M. M. Malamud & V. V. Peller

  3. Institut für Angewandte Analysis und Stochastik, Berlin, Germany

    H. Neidhardt

  4. Department of Mathematics, Michigan State University, Michigan, USA

    V. V. Peller

Authors
  1. M. M. Malamud
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  2. H. Neidhardt
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  3. V. V. Peller
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Correspondence to M. M. Malamud.

Additional information

To the memory of M. S. Agranovich, a remarkable mathematician and a remarkable personality

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 51, No. 3, pp. 33–55, 2017

Original Russian Text Copyright © by M. M. Malamud, H. Neidhardt, and V. V. Peller

The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number No. 02.A03.21.0008); the research of the third author is partially supported by NSF grant DMS 1300924

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Malamud, M.M., Neidhardt, H. & Peller, V.V. Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions. Funct Anal Its Appl 51, 185–203 (2017). https://doi.org/10.1007/s10688-017-0183-2

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  • DOI: https://doi.org/10.1007/s10688-017-0183-2

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