Transition probabilities and trace functions for $C^*$-algebras.

Endomorphisms of stable continuous-trace C-algebras

We classify spectrum-preserving endomorphisms of stable continuoustrace C∗-algebras up to inner automorphism by a surjective multiplicative invariant taking values in finite dimensional vector bundles over the spectrum. Specializing to automorphisms, this gives a different approach to results of Phillips and Raeburn. 2000 Mathematics Subject Classification: 46L05, 46M20

A Suspension Theorem for Continuous Trace C # -Algebras

Let B be a stable continuous trace C*-algebra with spectrum Y . We prove that the natural suspension map S, : [Co(X), B ] -+ [Co(X)@ Co(R), B @ Co(R)] is a bijection, provided that both X and Y are locally compact connected spaces whose one-point compactifications have the homotopy type of a finite CW-complex and X is noncompact. This is used to compute the second homotopy group of 9 in terms o...

And Dimension Functions on C * -algebras

We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C∗-algebras. In particular, our results apply to the largest class of simple C∗-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott’s classification program, proving that the u...

Transition Probabilities for Continual

The trace on the K-theory of group C∗-algebras

The canonical trace on the reduced C∗-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C∗-algebra to the real numbers. This paper studies the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture together with Atiyah’s L-index theorem implies that the range consists of the integers. We give a direct and elementary proof that if G acts ...