Everyone welcome.  Refreshments will be served in the Math Lounge before the exam.

Monday, May 28, 2012, 11:10 a.m., in BA 6183, 40 St. George Street

PhD Candidate:  Henning Petzka

PhD Advisor:  George A. Elliott

Thesis Title:  Stably non-stable C*-algebras with no bounded trace

Thesis Abstract:

A well-known theorem of Blackadar and Handelman states that every unital stably
finite C*-algebra has a bounded quasitrace. Rather strong generalizations of
stable finiteness to the non-unital case can be obtained by either requiring
the multiplier algebra to be stably finite, or alternatively requiring it to be
at least stably not properly infinite. My thesis deals with the question whether
the Blackadar-Handelman result can be extended to the non-unital case with
respect to these generalizations of stably finiteness.

For suitably well-behaved C*-algebras there is a positive result, but none of
the non-unital versions holds in full generality. Two examples of C*-algebras
are constructed. The first one is a non-unital, stably commutative C*-algebra
A that contradicts the weakest possible generalization of the Blackadar-Handelman
theorem: The multiplier algebras of all matrix algebras over A are finite,
while A has no bounded quasitrace. The second example is a non-unital, simple
C*-algebra B that is stably non-stable, i.e. no matrix algebra over B is a stable
C*-algebra. In fact, the multiplier algebras over all matrix algebras of this 
C*-algebra are not properly infinite. Moreover, the C*-algebra B has no bounded
quasitrace and therefore gives a simple counterexample to a possible 
generalization of the Blackadar-Handelman theorem.

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