Absolute continuity of spectral shift
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2018
- DOI:
- 10.48550/arXiv.1802.10243
- arXiv:
- arXiv:1802.10243
- Bibcode:
- 2018arXiv180210243M
- Keywords:
-
- Mathematics - Functional Analysis;
- Mathematics - Classical Analysis and ODEs;
- Mathematics - Complex Variables;
- Mathematics - Spectral Theory;
- 47A55;
- 47B10;
- 47A60;
- 47A63;
- 47B25;
- 47B44
- E-Print:
- 40 pages