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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
DOI: https://doi.org/10.1090/S0002-9939-06-08334-1
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

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.