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 |
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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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