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This article is cited in 10 scientific papers (total in 10 papers)
Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions
M. M. Malamudab, H. Neidhardtc, V. V. Pellerbd a Institute of Applied Mathematics and Mechanics NAS of Ukraine, Donetsk, Ukraine
b People’s Friendship University of Russia (RUDN University), Moscow, Russia
c Institut für Angewandte Analysis und Stochastik, Berlin, Germany
d Department of Mathematics, Michigan State University, Michigan, USA
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 $\boldsymbol\xi$ in $L^1(\mathbb{T})$ (called a spectral shift function for the pair $\{T_1,T_0\}$) such that the trace formula $\operatorname{trace}(f(T_1)-f(T_0))=\int_{\mathbb{T}} f'(\zeta)\boldsymbol{\xi}(\zeta)\,d\zeta$ holds for an arbitrary operator Lipschitz function $f$ analytic in the unit disk.
Keywords:
contraction, dissipative operator, trace formulae, spectral shift function, operator Lipschitz functions, perturbation determinant.
Received: 01.05.2017
Citation:
M. M. Malamud, H. Neidhardt, V. V. Peller, “Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions”, Funktsional. Anal. i Prilozhen., 51:3 (2017), 33–55; Funct. Anal. Appl., 51:3 (2017), 185–203
Linking options:
https://www.mathnet.ru/eng/faa3472https://doi.org/10.4213/faa3472 https://www.mathnet.ru/eng/faa/v51/i3/p33
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Abstract page: | 1858 | Full-text PDF : | 52 | References: | 38 | First page: | 34 |
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