Geodesic
Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 33-55

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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, spectral shift function, operator Lipschitz functions
Mots-clés : trace formulae, perturbation determinant. 
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     author = {M. M. Malamud and H. Neidhardt and V. V. Peller},
     title = {Analytic operator {Lipschitz} functions in the disk and a trace formula for functions of contractions},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {33--55},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a2/}
}
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M. M. Malamud; H. Neidhardt; V. V. Peller. Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 33-55. http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a2/