International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 671-680
doi:10.1155/S0161171294000955

Bundles of Banach algebras

J. W. Kitchen1 and D. A. Robbins2

1Department of Mathematics, Duke University, Durham 27706, NC, USA
2Department of Mathematics, Trinity College, Hartford 06106, CT, USA

Received 23 October 1992; Revised 20 April 1993

Copyright © 1994 J. W. Kitchen and D. A. Robbins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study bundles of Banach algebras π:A→X, where each fiber Ax=π−1({x}) is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra Γ(π) relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle π:A→X relates to the standard adjunction of identities to the fibers.