Email this article Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions
- Authors: Malamud M.M.1,2, Neidhardt H.3, Peller V.V.4,2
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Affiliations:
- Institute of Applied Mathematics and Mechanics NAS of Ukraine
- People’s Friendship University of Russia (RUDN University)
- Institut für Angewandte Analysis und Stochastik
- Department of Mathematics, Michigan State University
- Issue: Vol 51, No 3 (2017)
- Pages: 185-203
- Section: Article
- URL: https://journal-vniispk.ru/0016-2663/article/view/234328
- DOI: https://doi.org/10.1007/s10688-017-0183-2
- ID: 234328
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Abstract
In this paper we prove that for an arbitrary pair {T1, T0} of contractions on Hilbert space with trace class difference, there exists a function ξ in L1(T) (called a spectral shift function for the pair {T1, T0}) such that the trace formula trace(f(T1) − f(T0)) = ∫Tf′(ζ)ξ(ζ)dζ holds for an arbitrary operator Lipschitz function f analytic in the unit disk.
About the authors
M. M. Malamud
Institute of Applied Mathematics and Mechanics NAS of Ukraine; People’s Friendship University of Russia (RUDN University)
Author for correspondence.
Email: malamud3m@gmail.com
Ukraine, Donetsk; Moscow
H. Neidhardt
Institut für Angewandte Analysis und Stochastik
Email: malamud3m@gmail.com
Germany, Berlin
V. V. Peller
Department of Mathematics, Michigan State University; People’s Friendship University of Russia (RUDN University)
Email: malamud3m@gmail.com
United States, Michigan; Moscow
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