From: BrendaSueCook (brenda@math.missouri.edu)
Date: Fri Mar 30 2007 - 08:37:33 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 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 Supervisor: Konstantin A. Makarov
Wednesday, April 4
4:00 p.m.
312 Math Sciences Building
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