Herz-Schur multipliers and weakly almost periodic functions on locally compact groups

Xu, Guangwu

doi:10.1090/S0002-9947-97-01733-9

Herz-Schur multipliers and weakly almost periodic functions on locally compact groups
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Trans. Amer. Math. Soc. 349 (1997), 2525-2536 Request permission

Abstract:

For a locally compact group $G$ and $1<p<\infty$, let $A_{p}(G)$ be the Herz–Figà-Talamanca algebra and $B_{p}(G)$ the Herz-Schur multipliers of $G$, and $MA_{p}(G)$ the multipliers of $A_{p}(G)$. Let $W(G)$ be the algebra of continuous weakly almost periodic functions on $G$. In this paper, we show that (1), if $G$ is a noncompact nilpotent group or a noncompact [IN]-group, then $W(G)/B_{p}(G)^{-}$ contains a linear isometric copy of $l^{\infty }({\mathbb {N}})$; (2), for a noncommutative free group $F, B_{p}(F)$ is a proper subset of ${MA_{p}(F)\cap {W(F)}}$.

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