From: BrendaSueCook (brenda@math.missouri.edu)
Date: Tue Apr 03 2007 - 08:18:15 CDT
Ph.D. DEFENSE
Department of Mathematics
Anna Skripka
University of Missouri-Columbia
Trace Formulae in Finite von Neumann Algebras
Abstract: I will discuss 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 the
Krein 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. 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 integrated density of states.
Dissertation Advisor: Konstantin A. Makarov
Wednesday, April 4
4:00 p.m.
312 Math Sciences Building
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