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

 

Open subgroups and the centre problem for the Fourier algebra


Author: Zhiguo Hu
Journal: Proc. Amer. Math. Soc. 134 (2006), 3085-3095
MSC (2000): Primary 22D25, 43A30
Published electronically: May 5, 2006
MathSciNet review: 2231636
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Abstract: Let $ A(G)$ be the Fourier algebra of a locally compact group and $ UCB(\hat{G})$ the $ C^*$-algebra of uniformly continuous linear functionals on $ A(G)$. We study how the centre problem for the algebra $ UCB(\hat{G})^*$ (resp. $ A(G)^{**}$) is related to the centre problem for the algebras $ UCB(\hat{H})^*$ (resp. $ A(H)^{**}$) of $ \sigma$-compact open subgroups $ H$ of $ G$. We extend some results of Lau-Losert on the centres of $ UCB(\hat{G})^*$ and $ A(G)^{**}$.


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Additional Information

Zhiguo Hu
Affiliation: Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada N9B 3P4
Email: zhiguohu@uwindsor.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08334-1
PII: S 0002-9939(06)08334-1
Keywords: Fourier algebra, reduced Fourier-Stieltjes algebra
Received by editor(s): January 11, 2005
Received by editor(s) in revised form: May 5, 2005
Published electronically: May 5, 2006
Additional Notes: This research was supported by an NSERC grant.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.