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Isomorphisms between the second duals of group algebras of locally compact groups

Published online by Cambridge University Press:  24 October 2008

Hamid-Reza Farhadi
Hamid-Reza Farhadi
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, CanadaR3T 2N2
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Abstract

Let G be a locally compact group and L1(G) be the group algebra of G. We show that G is abelian or compact if every continuous automorphism of L1(G)** maps L1(G) onto L1(G) This characterizes all groups with this property and answers a question raised by F. Ghahramani and A. T. Lau in [7]. We also show that if G is a compact group and θ is any (algebra) isomorphism from L1(G)** onto L1(H)**, then H is compact and θ maps L1(G) onto L1(H).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 4 , May 1996 , pp. 657 - 663
Copyright
Copyright © Cambridge Philosophical Society 1996

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