Spectral averaging for trace compatible operators
Functional Analysis
2007-06-13 v2 Spectral Theory
Abstract
In this note the notions of trace compatible operators and infinitesimal spectral flow are introduced. We define the spectral shift function as the integral of infinitesimal spectral flow. It is proved that the spectral shift function thus defined is absolutely continuous and Krein's formula is established. Some examples of trace compatible affine spaces of operators are given.
Keywords
Cite
@article{arxiv.0704.1683,
title = {Spectral averaging for trace compatible operators},
author = {Nurulla Azamov and Fyodor Sukochev},
journal= {arXiv preprint arXiv:0704.1683},
year = {2007}
}
Comments
10 pages, LaTeX; a gap in the proof of Proposition 2.4 has been fixed