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The continuity of derivations and module homomorphisms

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

G. A. Willis
G. A. Willis
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia B3H 4H8, Canada
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Abstract

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This paper is concerned with the problem of automatic continuity of derivations from group algebras L1(G) is a locally compact group, and convolution algebras L1(ω), where ω is a weight function. In the case of group algebras, it is shown that either the problem reduces to the case when G is the free group on a countably infinite number of generators or there is a non-discrete group G with a discontinuous l1(G)-bimodule homomorphism from L1(G). It is also shown that every derivation from L1(G) to a commutative L1(G)-bimodule is continuous. Similar results are obtained for weighted convolution algebras.

MSC classification

Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 3 , June 1986 , pp. 299 - 320
Copyright
Copyright © Australian Mathematical Society 1986

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