Exact C*-bundles

Blanchard, R. and Wassermann, S. (2007) Exact C*-bundles. Houston Journal of Mathematics, 33(4), pp. 1147-1159.

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Abstract

Kirchberg and Wassermann showed that if A = {A, X, pi(x) : A -> 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 B = {B, X, pi(x) : A -> B-x} on X the minimal C-0(X)-amalgamated tensor product bundle A circle times(min)(C0(X)) 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 A circle times(max)(C0(X)) B is continuous for all continuous C*-bundles B on X if and only if A has nuclear bundle C*-algebra.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:UNSPECIFIED
Authors: Blanchard, R., and Wassermann, S.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Houston Journal of Mathematics
Publisher:University of Houston
ISSN:0362-1588

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