Exact C*-Bundles

• Autores: Etienne Blanchard, Simon Wassermann
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 4, 2007, págs. 1147-1159
• Idioma: inglés
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• Resumen

  • 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.