Functional Analysis and Its Applications

, Volume 51, Issue 3, pp 185–203 | Cite as

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

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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.

Key words

contraction dissipative operator trace formulae spectral shift function operator Lipschitz functions perturbation determinant 
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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and Mechanics NAS of UkraineDonetskUkraine
  2. 2.People’s Friendship University of Russia (RUDN University)MoscowRussia
  3. 3.Institut für Angewandte Analysis und StochastikBerlinGermany
  4. 4.Department of MathematicsMichigan State UniversityMichiganUSA

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