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The centre of the second conjugate algebra of the Fourier algebra for infinite products of groups

Published online by Cambridge University Press:  03 February 2005

ANTHONY TO-MING LAU  and
VIKTOR LOSERT
ANTHONY TO-MING LAU
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6R 1T1, Canada. e-mail: [email protected]
VIKTOR LOSERT
Affiliation:
Institut für Mathematik, Universität Wien, A-1090 Wien, Strudhofgasse 4, Vienna, Austria. e-mail: [email protected]
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Abstract

In this paper, we shall prove that if $G$ is a countably infinite product of second countable amenable locally compact groups $G_i,i\,{=}\,0,1,2,\dots$ and each $G_i$ is a non-trivial compact group for $i>0,$ then the center of the second conjugate algebra of the Fourier algebra $A(G)$ of $G$ is precisely $A(G)$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 1 , January 2005 , pp. 27 - 39
Copyright
2005 Cambridge Philosophical Society

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