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FACTORIZATION IN FINITE-CODIMENSIONAL IDEALS OF GROUP ALGEBRAS

Published online by Cambridge University Press:  20 August 2001

GEORGE A. WILLIS
GEORGE A. WILLIS
Affiliation:
Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, [email protected]
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Abstract

Let $G$ be a $\sigma$-compact, locally compact group and $\mathcal I$ be a closed 2-sided ideal with finite codimension in $L^1(G)$. It is shown that there are a closed left ideal ${\mathcal L}$ having a right bounded approximate identity and a closed right ideal ${\mathcal R}$ having a left bounded approximate identity such that ${\mathcal I} = {\mathcal L} + {\mathcal R}$. The proof uses ideas from the theory of boundaries of random walks on groups. 2000 Mathematics Subject Classification: primary 43A20; secondary 42A85, 43A07, 46H10, 46H40, 60B11.

Keywords

amenableidealgroup algebrabounded approximate identityrandom walkfactorizationautomatic continuity
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 82 , Issue 3 , May 2000 , pp. 676 - 700
Copyright
2001 London Mathematical Society

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