The Radon-Nikodym property for some Banach algebras related to the Fourier algebra

Granirer, Edmond

doi:10.1090/S0002-9939-2011-10853-0

The Radon-Nikodym property for some Banach algebras related to the Fourier algebra
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by Edmond E. Granirer

Proc. Amer. Math. Soc. 139 (2011), 4377-4384

DOI: https://doi.org/10.1090/S0002-9939-2011-10853-0

Published electronically: April 22, 2011

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Abstract:

The Radon-Nikodym property for the Banach algebras $A_p^r(G)=A_p\cap L^r(G)$, where $A_2(G)$ is the Fourier algebra, is investigated. A complete solution is given for amenable groups $G$ if $1<p<\infty$ and for arbitrary $G$ if $p=2$ and $A_2(G)$ has a multiplier bounded approximate identity. The results are new even for $G=\mathbb {R}^n$.

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