International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 671-680
Bundles of Banach algebras
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.
We study bundles of Banach algebras , where each fiber is a Banach algebra and is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle relates to the standard adjunction of identities to the fibers.