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

Feinstein, J. F. and Kaniuth, E. (1999) Spectral synthesis and topologies on ideal spaces for Banach *-algebras.

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Abstract

Abstract This paper continues the study of spectral synthesis and the topologies Tau-infinity and

Tau-r on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras,

and in particular on L 1 -group algebras. It is shown that if a group G is a infnite extension of

an abelian group then Tau-r is Hausdorff on the ideal space of L 1 (G) if and only if L 1 (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 L 1 (G) has spectral synthesis. It is also shown that if G is

a non-discrete group then Tau-r is not Hausdorff on the ideal lattice of the Fourier algebra

A(G).

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Gardner, Mike
Date Deposited: 30 Jul 2001
Last Modified: 22 Jun 2011 07:21
URI: http://eprints.nottingham.ac.uk/id/eprint/15

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