ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46, 19, 22 Troitsky, Evgenij, Moscow State University, Russia Kuiper and Dixmier-Douady theorems for C*-Hilbert modules and K-theory Let A be a σ-unital C*-algebra, l_{2}(A) be the standard C*-Hilbert A-module, GL(A) and GL^{∗}(A) be the groups of bounded A-isomorphisms and bounded A-isomorphisms admitting an adjoint, respectively. Considering them as left and two-sided multipliers of A-compact operators on l_{2}(A) we can introduce the corresponding left strict topology. First we get a simple proof of the Cuntz-Higson theorem on the norm contractibility of GL^{∗}(A). We prove the norm contractibility of GL(A) for some classes of algebras (e. g., A ⊂ K(H), A = C_{0}(M), where M is finite dimensional). We prove some generalizations of the Dixmier-Douady theorem to the left strict topology. Then we apply the results in K-theory.