Arens regularity of ideals in $A(G)$, $A_{cb}(G)$ and $A_M(G)$
Functional Analysis
2023-02-14 v1
Abstract
In this paper, we look at the question of when various ideals in the Fourier algebra or its closures and in, respectively, its multiplier and -multiplier algebra are Arens regular. We show that in each case, if a non-zero ideal is Arens regular, then the underlying group must be discrete. In addition, we show that if an ideal in has a bounded approximate identity, then it is Arens regular if and only if it is finite-dimensional.
Keywords
Cite
@article{arxiv.2302.05699,
title = {Arens regularity of ideals in $A(G)$, $A_{cb}(G)$ and $A_M(G)$},
author = {Brian Forrest and John Sawatzky and Aasaimani Thamizhazhagan},
journal= {arXiv preprint arXiv:2302.05699},
year = {2023}
}