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The continuity of derivations from group algebras: factorizable and connected groups

Part of: Abstract harmonic analysis Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

George Willis
George Willis
Affiliation:
Mathematics Research SectionSchool of Mathematical Sciences Australian National UniversityGPO Box 4, Canberra ACT 2601, Australia
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Abstract

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A group is said to be factorizable if it has a finite number of abelian subgroups, H1, H2, … Hn, such that G = H1H2 … Hn. It is shown that, if G is a factorizable or connected locally compact group, then every derivation from L1 (G) to an arbitrary L1 (G)-bimodule X is continuous.

Keywords

factorizationgroup algebraautomatic continuityderivation.

MSC classification

Secondary: 46H05: General theory of topological algebras 46H10: Ideals and subalgebras 43A20: $L^1$-algebras on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 2 , April 1992 , pp. 185 - 204
Copyright
Copyright © Australian Mathematical Society 1992

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