Trace formulae in finite von Neumann algebras
Metadata[+] Show full item record
The dissertation is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for the [xi]-index, a spectral parameter independent counterpart of Krein's spectral shift function. The proofs of the main results are based on diverse properties of the operator logarithm and argument averaged with respect to a normal tracial state that are derived in this work. In addition, formula representations for the [xi]-index and the [xi]- function are obtained and the concept of the [xi]-index is related to that of the spectrum distribution function for some random operators.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.