Abstract
This is a study of Arens regularity in the context of quotients of the Fourier algebra on a non-discrete locally compact abelian group (or compact group).
(1) If a compact set $E$ of $G$ is of bounded synthesis and is the support of a pseudofunction, then $A(E)$ is weakly sequentially complete. (This implies that every point of $E$ is a Day point.)
(2) If a compact set $E$ supports a synthesizable pseudofunction, then $A(E)$ has Day points. (The existence of a Day point implies that $A(E)$ is not Arens regular.)
We use be $L^{2}$-methods of proof which do not have obvious extensions to the case of $A_{p}(E)$.
Related results, context (historical and mathematical), and open questions are given.
Citation
Colin C. Graham. "Arens regularity and weak sequential completeness for quotients of the Fourier algebra." Illinois J. Math. 44 (4) 712 - 740, Winter 2000. https://doi.org/10.1215/ijm/1255984689
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