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

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Funktsional'nyi Analiz i ego Prilozheniya, 2017, Volume 51, Issue 3, Pages 33–55
DOI: https://doi.org/10.4213/faa3472 (Mi faa3472)

This article is cited in 12 scientific papers (total in 12 papers)

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

M. M. Malamud^ab, H. Neidhardt^c, V. V. Peller^bd

^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

Full-text PDF (343 kB) Citations (12)

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DOI: https://doi.org/10.4213/faa3472

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.

Received: 01.05.2017

English version:
Functional Analysis and Its Applications, 2017, Volume 51, Issue 3, Pages 185–203
DOI: https://doi.org/10.1007/s10688-017-0183-2

Bibliographic databases:

Document Type: Article

UDC: 517.983.24

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/faa3472

https://doi.org/10.4213/faa3472

https://www.mathnet.ru/eng/faa/v51/i3/p33

This publication is cited in the following 12 articles:

V. V. Peller, “Besov spaces in operator theory”, Russian Math. Surveys, 79:1 (2024), 1–52
Arup Chattopadhyay, Soma Das, Chandan Pradhan, “Second‐order trace formulas”, Mathematische Nachrichten, 2024
A. R. Aliev, E. H. Eyvazov, “Spectral Shift Function and Eigenvalues of the Perturbed Operator”, J Math Sci, 282:4 (2024), 464
M. M. Malamud, H. Neidhardt, V. V. Peller, “Real-Valued Spectral Shift Functions for Contractions and Dissipative Operators”, Dokl. Math., 2024
M. M. Malamud, H. Neidhardt, V. V. Peller, “The reality of spectral shift functions for contractions and dissipative operators”, Dokl. RAN. Math. Inf. Proc. Upr., 519 (2024), 28–32
A. Chattopadhyay, S. Das, Ch. Pradhan, “The Koplienko–Neidhardt trace formula for unitaries — a new proof”, J. Math. Anal. Appl., 505:1 (2022), 125467
A. R. Aliev, E. Kh. Eivazov, “Funktsiya spektralnogo sdviga i sobstvennye znacheniya vozmuschennogo operatora”, Issledovaniya po lineinym operatoram i teorii funktsii. 50, Zap. nauchn. sem. POMI, 512, POMI, SPb., 2022, 15–26
A. R. Mirotin, “Lifshitz-Krein trace formula for Hirsch functional calculus on Banach spaces”, Complex Anal. Oper. Theory, 13:3 (2019), 1511–1535
M. M. Malamud, H. Neidhardt, V. V. Peller, “Absolute continuity of spectral shift”, J. Funct. Anal., 276:5 (2019), 1575–1621
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
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, 113
Mirotin A.R., “Bernstein Functions of Several Semigroup Generators on Banach Spaces Under Bounded Perturbations, II”, Oper. Matrices, 12:2 (2018), 445–463

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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