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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171294000955 |
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| _version_ | 1849307692882984960 |
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| 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 |