Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions |
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| Authors: | M M Malamud H Neidhardt V V Peller |
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| Institution: | 1.Institute of Applied Mathematics and Mechanics NAS of Ukraine,Donetsk,Ukraine;2.People’s Friendship University of Russia (RUDN University),Moscow,Russia;3.Institut für Angewandte Analysis und Stochastik,Berlin,Germany;4.Department of Mathematics,Michigan State University,Michigan,USA |
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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. |
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