English

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