Resumen de Exact C*-Bundles

Etienne Blanchard, Simon Wassermann

• Kirchberg and Wassermann showed that if A is an exact continuous C*- bundle on a locally compact Hausdorff space X, then for any other continuous C*-bundle B on X, the minimal tensor product bundle amalgamated over C0(X) of A and B is again continuous. In this paper it is shown conversely that this property characterises the continuous C*-bundles with exact bundle C*-algebra when the base space X has no isolated points. For such X a corresponding result for the maximal tensor product amalgamated over C0(X) of C*-bundles on X is also shown to hold, namely that the maximal tensor product amalgamated over C0(X) of A and B is continuous for all continuous C*-bundles B on X if and only if A has nuclear bundle C*-algebra.