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Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 3, Pages 33–55 (Mi faa3472)  

This article is cited in 5 scientific papers (total in 5 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.A03.21.0008
National Science Foundation DMS 1300924
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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English version:
Functional Analysis and Its Applications, 2017, 51:3, 185–203

Bibliographic databases:

UDC: 517.983.24
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

Citation in format AMSBIB
\by M.~M.~Malamud, H.~Neidhardt, V.~V.~Peller
\paper Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions
\jour Funktsional. Anal. i Prilozhen.
\yr 2017
\vol 51
\issue 3
\pages 33--55
\jour Funct. Anal. Appl.
\yr 2017
\vol 51
\issue 3
\pages 185--203

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    This publication is cited in the following articles:
    1. Mirotin A.R., “Bernstein Functions of Several Semigroup Generators on Banach Spaces Under Bounded Perturbations, II”, Oper. Matrices, 12:2 (2018), 445–463  crossref  mathscinet  zmath  isi  scopus
    2. A. R. Mirotin, “Lifshitz-Krein trace formula for Hirsch functional calculus on Banach spaces”, Complex Anal. Oper. Theory, 13:3 (2019), 1511–1535  crossref  isi
    3. M. M. Malamud, H. Neidhardt, V. V. Peller, “Absolute continuity of spectral shift”, J. Funct. Anal., 276:5 (2019), 1575–1621  crossref  isi
    4. A. B. Aleksandrov, V. V. Peller, D. S. Potapov, “On a Trace Formula for Functions of Noncommuting Operators”, Math. Notes, 106:4 (2019), 481–487  mathnet  crossref  crossref  mathscinet  isi  elib
    5. A. Skripka, A. Tomskova, “Multilinear operator integrals theory and applications preface”: Skripka, A Tomskova, A, Multilinear Operator Integrals: Theory and Applications, Lect. Notes Math., Lecture Notes in Mathematics, 2250, Springer, 2019, V+  mathscinet  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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