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Groups and semigroups in analysis: a conference in honour of J.S. Pym on the occasion of his retirement
May 30 - June 1, 2003
University of Sheffield
Sheffield, UK

Organizers
A. Lau, University of Alberta; P. Milnes, University of Western Ontario; R. Sharp, University of Sheffield; D. Strauss, University of Hull

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A short proof of The Glicksberg-Host-Parreau Theorem.
by
Ali Ulger
Koc University, Istanbul.

Let G be a locally compact abelian group, L1(G) be its group algebra and M(G) be its measure algebra. Fix a measure m in M(G). The Glicksberg-Host-Parreau Theorem states this: The ideal L1(G)*m is closed in L1(G) iff the measure m is the product of an invertible measure and an idempotent measure. Only one proof of this theorem is known [Ann. Inst. Fourier 23 (1978),143-164] and it is very long and very sofisticated. In this talk we present a very short (about 2-3 pages),self-contained and elementary proof of this important theorem. Moreover our proof also applies to some other Banach algebras such as the Fourier algebra A(G)of a locally compact amenable group G.

Date received: February 3, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cakn-02.