Bundles of Banach algebras

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 f...

Full description

Saved in:
Bibliographic Details
Main Authors: J. W. Kitchen, D. A. Robbins
Format: Article
Language:English
Published: Wiley 1994-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171294000955
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849307692882984960
author J. W. Kitchen
D. A. Robbins
author_facet J. W. Kitchen
D. A. Robbins
author_sort J. W. Kitchen
collection DOAJ
description 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.
format Article
id doaj-art-21c738b5a6824808a936baacbcc06f0b
institution Kabale University
issn 0161-1712
1687-0425
language English
publishDate 1994-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-21c738b5a6824808a936baacbcc06f0b2025-08-20T03:54:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117467168010.1155/S0161171294000955Bundles of Banach algebrasJ. W. Kitchen0D. A. Robbins1Department of Mathematics, Duke University, Durham 27706, NC, USADepartment of Mathematics, Trinity College, Hartford 06106, CT, USAWe 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.http://dx.doi.org/10.1155/S0161171294000955Banach bundlebundle of Banach algebrasGelfand representationfiber space.
spellingShingle J. W. Kitchen
D. A. Robbins
Bundles of Banach algebras
International Journal of Mathematics and Mathematical Sciences
Banach bundle
bundle of Banach algebras
Gelfand representation
fiber space.
title Bundles of Banach algebras
title_full Bundles of Banach algebras
title_fullStr Bundles of Banach algebras
title_full_unstemmed Bundles of Banach algebras
title_short Bundles of Banach algebras
title_sort bundles of banach algebras
topic Banach bundle
bundle of Banach algebras
Gelfand representation
fiber space.
url http://dx.doi.org/10.1155/S0161171294000955
work_keys_str_mv AT jwkitchen bundlesofbanachalgebras
AT darobbins bundlesofbanachalgebras