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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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Factorisation in finite codimensional ideals of group algebras
by
G. Willis
Newcastle, Australia

Let G be a locally compact group and let L1(G) be the group convolution algebra of G. Then for each closed cofinite ideal I in L1(G) there are a closed left ideal L with a right bounded approximate identity and a closed right ideal R with a left bounded approximate identity such that I = L+ R. Consequently, every element of I is a sum of two products.

The proof of this claim uses a random walk on G to prove a convolution estimate in L1(G). This estimate is then used to define the ideals L and R and their approximate identities.

Date received: May 26, 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-15.