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Open subgroups and the centre problem for the Fourier algebra

Author(s): Zhiguo Hu
Journal: Proc. Amer. Math. Soc. 134 (2006), 3085-3095.
MSC (2000): Primary 22D25, 43A30
Posted: May 5, 2006
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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: 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
Posted: May 5, 2006
Additional Notes: This research was supported by an NSERC grant.
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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