## Illinois Journal of Mathematics

### Arens regularity and weak sequential completeness for quotients of the Fourier algebra

Colin C. Graham

#### 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.

#### Article information

Source
Illinois J. Math., Volume 44, Issue 4 (2000), 712-740.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255984689

Digital Object Identifier
doi:10.1215/ijm/1255984689

Mathematical Reviews number (MathSciNet)
MR1804322

Zentralblatt MATH identifier
0963.43001

#### Citation

Graham, Colin C. Arens regularity and weak sequential completeness for quotients of the Fourier algebra. Illinois J. Math. 44 (2000), no. 4, 712--740. doi:10.1215/ijm/1255984689. https://projecteuclid.org/euclid.ijm/1255984689