RATIONAL -STABILITY OF CONTINUOUS -ALGEBRAS

Abstract

We show that the properties of being rationally K-stable passes from the fibres of a continuous $C(X)$ -algebra to the ambient algebra, under the assumption that the underlying space X is compact, metrizable, and of finite covering dimension. As an application, we show that a crossed product C*-algebra is (rationally) K-stable provided the underlying C*-algebra is (rationally) K-stable, and the action has finite Rokhlin dimension with commuting towers.