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Spectral synthesis and topologies on ideal spaces for Banach *-algebras

Feinstein, Joel; Kaniuth, E.; Somerset, D.W.B.

Authors

Joel Feinstein

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
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Peer Reviewed Not Peer Reviewed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
Institution 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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Copyright Statement
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