Absolute continuity of spectral shift
Functional Analysis
2018-03-01 v1 Classical Analysis and ODEs
Complex Variables
Spectral Theory
Abstract
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 spectrum 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.
Keywords
Cite
@article{arxiv.1802.10243,
title = {Absolute continuity of spectral shift},
author = {Mark Malamud and Hagen Neidhardt and Vladimir Peller},
journal= {arXiv preprint arXiv:1802.10243},
year = {2018}
}
Comments
40 pages