## Edmond E. Granirer, Functional analytic properties of some Banach algebras related to the Fourier algebra

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Volume 1, Issue 3, 1 December 2017, Pages 299-306

Abstract. This is a survey of some functional analytic properties of the Banach algebras $A_p^r(G)=A_p\cap L^r(G)$ for locally compact groups $G$ obtained in [18,19, 20, 21]. These include Arens regularity, strict containment for fixed $p$ and increasing $r$, the RNP and optimisation in $A_p^r(G)$, weak sequential completeness, spectral synthesis, etc. It is found that $A_p^r(G)$ behaves very differently from $A_p(G)$, if $r<\infty$. The results are new even if $G=R$ or $G=Z$, the real line or the additive integers.