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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weak amenability and the second dual
of the Fourier algebra


Author: Brian Forrest
Journal: Proc. Amer. Math. Soc. 125 (1997), 2373-2378
MSC (1991): Primary 46H20; Secondary 43A20
MathSciNet review: 1389517
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Abstract: Let $G$ be a locally compact group. We will consider amenability and weak amenability for Banach algebras which are quotients of the second dual of the Fourier algebra. In particular, we will show that if $A(G)^{**}$ is weakly amenable, then $G$ has no infinite abelian subgroup.


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Additional Information

Brian Forrest
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03844-6
PII: S 0002-9939(97)03844-6
Keywords: Fourier algebra, second dual, weakly amenable Banach algebra
Received by editor(s): June 5, 1995
Received by editor(s) in revised form: February 26, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society