Illinois Journal of Mathematics

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

Colin C. Graham

Full-text: Open access

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


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