English

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 A(G)A(G) or its closures AM(G)A_M(G) and Acb(G)A_{cb}(G) in, respectively, its multiplier and cbcb-multiplier algebra are Arens regular. We show that in each case, if a non-zero ideal is Arens regular, then the underlying group GG must be discrete. In addition, we show that if an ideal II in A(G)A(G) 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}
}