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
