Exact C*-bundles
Résumé
Kirchberg and Wassermann showed that if $\mathcal{A}=\{A,X,\pi_x:A\to A_x\}$ is a continuous C*-bundle on a locally compact Hausdorff space $X$ with exact bundle C*-algebra $A$, then for any other continuous C*-bundle $\mathcal{B}=\{B,X,\pi_x:A\to B_x\}$ on $X$ the minimal $C_0(X)$-amalgamated tensor product bundle $\mathcal{A}\otimes^{min}_{C_0(X)} \mathcal{B}$ is again continuous. In this paper it is shown conversely that this property characterises the continuous C*-bundles which have exact bundle C*-algebras when the base space $X$ has no isolated points. For such $X$ a corresponding result for the maximal $C_0(X)$-amalgamated tensor product of C*-bundles on $X$ is also shown to hold, namely that $\mathcal{A}\otimes^{max}_{C_0(X)} \mathcal{B}$ is continuous for all continuous C*-bundles $B$ on $X$ if and only if $\mathcal{A}$ has nuclear bundle C*-algebra.
Domaines
Algèbres d'opérateurs [math.OA]
Origine : Fichiers produits par l'(les) auteur(s)
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