Spectral synthesis and topologies on ideal spaces for Banach *-algebras
This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdo...
| Main Authors: | , , |
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| Format: | Article |
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Elsevier
2002
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| Online Access: | https://eprints.nottingham.ac.uk/15/ |
| _version_ | 1848790350227832832 |
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| author | Feinstein, Joel Kaniuth, E. Somerset, D.W.B. |
| author_facet | Feinstein, Joel Kaniuth, E. Somerset, D.W.B. |
| author_sort | Feinstein, Joel |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G). |
| first_indexed | 2025-11-14T18:11:13Z |
| format | Article |
| id | nottingham-15 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:11:13Z |
| publishDate | 2002 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-152020-05-04T16:25:41Z https://eprints.nottingham.ac.uk/15/ Spectral synthesis and topologies on ideal spaces for Banach *-algebras Feinstein, Joel Kaniuth, E. Somerset, D.W.B. This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G). Elsevier 2002-12-01 Article NonPeerReviewed Feinstein, Joel, Kaniuth, E. and Somerset, D.W.B. (2002) Spectral synthesis and topologies on ideal spaces for Banach *-algebras. Journal of Functional Analysis, 196 (1). pp. 19-39. ISSN 0022-1236 http://www.sciencedirect.com/science/article/pii/S0022123602939649 doi:10.1006/jfan.2002.3964 doi:10.1006/jfan.2002.3964 |
| spellingShingle | Feinstein, Joel Kaniuth, E. Somerset, D.W.B. Spectral synthesis and topologies on ideal spaces for Banach *-algebras |
| title | Spectral synthesis and topologies on ideal spaces for Banach *-algebras |
| title_full | Spectral synthesis and topologies on ideal spaces for Banach *-algebras |
| title_fullStr | Spectral synthesis and topologies on ideal spaces for Banach *-algebras |
| title_full_unstemmed | Spectral synthesis and topologies on ideal spaces for Banach *-algebras |
| title_short | Spectral synthesis and topologies on ideal spaces for Banach *-algebras |
| title_sort | spectral synthesis and topologies on ideal spaces for banach *-algebras |
| url | https://eprints.nottingham.ac.uk/15/ https://eprints.nottingham.ac.uk/15/ https://eprints.nottingham.ac.uk/15/ |