Joel Feinstein
Spectral synthesis and topologies on ideal spaces for Banach *-algebras
Feinstein, Joel; Kaniuth, E.; Somerset, D.W.B.
Authors
E. Kaniuth
D.W.B. Somerset
Abstract
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).
Journal Article Type | Article |
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Publication Date | Dec 1, 2002 |
Journal | Journal of Functional Analysis |
Print ISSN | 0022-1236 |
Electronic ISSN | 0022-1236 |
Publisher | Elsevier |
Peer Reviewed | Not Peer Reviewed |
Volume | 196 |
Issue | 1 |
APA6 Citation | Feinstein, J., Kaniuth, E., & Somerset, D. (2002). Spectral synthesis and topologies on ideal spaces for Banach *-algebras. Journal of Functional Analysis, 196(1), doi:10.1006/jfan.2002.3964 |
DOI | https://doi.org/10.1006/jfan.2002.3964 |
Publisher URL | http://www.sciencedirect.com/science/article/pii/S0022123602939649 |
Copyright Statement | Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf |
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