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

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 s...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 1996-05, Vol.119 (4), p.657-663
Main Author: Farhadi, Hamid-Reza
Format: Article
Language:English
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Summary: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).
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100074491