Weakly almost periodic functions and Fourier-Stieltjes algebras of locally compact groups

Chou, Ching

doi:10.1090/S0002-9947-1982-0670924-2

Weakly almost periodic functions and Fourier-Stieltjes algebras of locally compact groups
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Trans. Amer. Math. Soc. 274 (1982), 141-157 Request permission

Abstract:

A noncompact locally compact group $G$ is called an Eberlein group if $W(G) = B{(G)^ - }$ where $W(G)$ is the algebra of continuous weakly almost periodic functions on $G$ and $B{(G)^ - }$ is the uniform closure of the Fourier-Stieltjes algebra of $G$. We show that if $G$ is a noncompact $[IN]$-group or a noncompact nilpotent group then $W(G)/B{(G)^ - }$ contains a linear isometric copy of ${l^\infty }$. In particular, $G$ is not an Eberlein group. On the other hand, finite direct products of Euclidean motion groups and, by a result of W. Veech, noncompact semisimple analytic groups with finite centers are Eberlein groups.

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