A trace formula for functions of contractions and analytic operator Lipschitz functions [Une formule de trace pour les fonctions de contraction et les fonctions analytiques opérateurs-lipschitziennes]

In this note, we study the problem of evaluating the trace of f(T)−f(R), where T and R are contractions on a Hilbert space with trace class difference, i.e. T−R∈S1, and f is a function analytic in the unit disk D. It is well known that if f is an operator Lipschitz function analytic in D, then f(T)−f(R)∈S1. The main result of the note says that there exists a function ξ (a spectral shift function) on the unit circle T of class L1(T) such that the following trace formula holds: trace(f(T)−f(R))=∫Tf′(ζ)ξ(ζ)dζ, whenever T and R are contractions with T−R∈S1, and f is an operator Lipschitz function analytic in D. © 2017 Académie des sciences

Авторы
Malamud M. 1, 2 , Neidhardt H.3 , Peller V. 2, 4
Редакторы
-
Издательство
Elsevier Masson SAS
Номер выпуска
7
Язык
-
Страницы
806-811
Статус
Опубликовано
Подразделение
-
Номер
-
Том
355
Год
2017
Организации
  • 1 Institute of Applied Mathematics and Mechanics, NAS of Ukraine, Slavyansk, Ukraine
  • 2 RUDN University, 6 Miklukho-Maklay St., Moscow, 117198, Russian Federation
  • 3 Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, Berlin, 10117, Germany
  • 4 Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States
Ключевые слова
-
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5460/