Open subgroups and the centre problem for the Fourier algebra

Hu, Zhiguo

doi:10.1090/S0002-9939-06-08334-1

Open subgroups and the centre problem for the Fourier algebra
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Proc. Amer. Math. Soc. 134 (2006), 3085-3095 Request permission

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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