On spectral perturbation theory in von Neumann algebras.
by
Anna Skripka
Texas A&M University
Coauthors: K. A. Makarov

The standard spectral perturbation theory studies how the spectrum of an operator changes under a perturbation with discrete spectrum. Perturbations with non-trivial essential spectra can be handled by passing to a general semi-finite von Neumann algebra setting. Continuous analogs of such important tools of the perturbation theory as the Krein spectral shift function, the Birman-Solomyak spectral averaging formula, and the Birman-Schwinger eigenvalue counting principle were recently obtained in the von Neumann algebra context. We use these tools and make further advances to derive monotonicity and convexity inequalities for operator functions inside a normal faithful semi-finite trace.

Date received: June 13, 2008