Weakly amenable groups and the RNP for some Banach algebras related to the Fourier algebra
Volume 130 / 2013
Colloquium Mathematicum 130 (2013), 19-26
MSC: Primary 43A15, 46J10, 43A25, 46B22; Secondary 46J20, 43A30, 43A80, 22E30.
DOI: 10.4064/cm130-1-2
Abstract
It is shown that if $G$ is a weakly amenable unimodular group then the Banach algebra $A_p^r(G)=A_p\cap L^r(G)$, where $A_p(G)$ is the Figà-Talamanca–Herz Banach algebra of $G$, is a dual Banach space with the Radon–Nikodym property if $1\leq r\leq \max(p,p')$. This does not hold if $p=2$ and $r>2$.
