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The Quarterly Journal of Mathematics 2001 52(1):13-24; doi:10.1093/qjmath/52.1.13
© 2001 by Oxford University Press
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Arens regularity and the second dual of certain quotients of the fourier algebra

Colin C. Graham1

1 RR#1-site, H-46, Bowen Island, British Columbia, V0N 1G0 Canada, e-mail: ccgraham{at}alum.mit.edu

We show that every metrizable locally compact abelian group contains a closed subset E such that the restriction A(E) of the Fourier algebra to E is Arens regular whatever the bounded multiplication it is given, but such that neither Ã(E) nor A(E)** is Arens regular (in their natural multiplications).

Received 30 April 1999. Revised 05 January 2000. Revised 11 April 2000.


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