Journal of Operator Theory

Volume 55, Issue 1, Winter 2006 pp. 169-183.

An abstract Pimsner-Popa-Voiculescu theorem

Authors: Dan Kucerovsky (1) and Ping Wong Ng (2)
Author institution: (1) Department of Mathematics and Statistics, UNB-F, Fredericton, N.B., Canada E3B 5A3
(2) Department of Mathematics and Statistics, UNB-F, Fredericton, N.B., Canada E3B 5A3

Summary: Let $A$ and $B_0$ be separable $C^{*}$-algebras with $B_0$ stable and containing a full projection. Let $X$ be a compact, finite-dimensional topological space. We show that if $\widehat{\tau }:A\rightarrow\Mul(C(X)\otimes B_0)$ is a unital, trivial extension such that $\widehat{\tau}_x$ is absorbing for every $x\in X$ then $\widehat{\tau}$ is absorbing. This generalizes a theorem by Pimnser, Popa, and Voiculescu. The main technical tool is a proposition showing that, under suitable conditions, a deformation of properly infinite projections is a properly infinite projection.

Keywords: $K$-theory, $C^{*}$-algebras

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