Absolute continuity of spectral shift

被引：12
|
作者：
Malamud, M. M. [1 ]
Neidhardt, H. [2 ]
Peller, V. V. [1 ,3 ]
机构：
[1] RUDN Univ, Peoples Friendship Univ Russia, 6 Miklukho Maklaya St, Moscow 6117198, Russia
[2] Inst Angew Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany
[3] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 276卷 / 05期
关键词：
Lifshits-Krein trace formula; Spectral shift function; Self-adjoint operators; Unitary operators; Contractions; Dissipative operators; TRACE FORMULA; UNITARY; OPERATORS; CONTRACTIONS; DETERMINANTS; PAIR;
D O I：
10.1016/j.jfa.2018.05.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish the absolute continuity of spectral shift, we use the Sz.-Nagy theorem on the absolute continuity of the spectral measure of the minimal unitary dilation of a completely nonunitary contraction. We also give a construction of an intermediate contraction for a pair of contractions with trace class difference. (C) 2018 Elsevier Inc. All rights reserved.
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页码：1575 / 1621
页数：47
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