## Illinois Journal of Mathematics

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

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

#### 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

**Subjects**

Primary: 43A45: Spectral synthesis on groups, semigroups, etc.

Secondary: 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 46J99: None of the above, but in this section

#### 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