Skip to main content

Research Repository

Advanced Search

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

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

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


Authors

E. Kaniuth

D.W.B. Somerset



Abstract

This paper continues the study of spectral synthesis and the topologies ?? and ?r 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 ?r 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 ?r is not Hausdorff on the ideal lattice of the Fourier algebra A(G).

Citation

Feinstein, J., Kaniuth, E., & Somerset, D. (2002). Spectral synthesis and topologies on ideal spaces for Banach *-algebras. Journal of Functional Analysis, 196(1), https://doi.org/10.1006/jfan.2002.3964

Journal Article Type Article
Acceptance Date Feb 26, 2002
Publication Date Dec 1, 2002
Deposit Date Jul 30, 2001
Publicly Available Date Mar 28, 2024
Journal Journal of Functional Analysis
Print ISSN 0022-1236
Electronic ISSN 0022-1236
Publisher Elsevier
Peer Reviewed Not Peer Reviewed
Volume 196
Issue 1
DOI https://doi.org/10.1006/jfan.2002.3964
Public URL https://nottingham-repository.worktribe.com/output/703039
Publisher URL http://www.sciencedirect.com/science/article/pii/S0022123602939649

Files






You might also like



Downloadable Citations