A note on a question of Garth Dales: Arens regularity as a three space property
Functional Analysis
2025-12-08 v3
Abstract
Garth Dales asked whether a Banach algebra having an Arens regular closed ideal with Arens regular quotient is necessarily Arens regular. We prove in this note that, for a class of Banach algebras including the standard algebras in harmonic analysis, Garth's conditions force the algebra to be even reflexive. We also give examples of Banach algebras with Garth's conditions, that are not Arens regular.
Cite
@article{arxiv.2407.09947,
title = {A note on a question of Garth Dales: Arens regularity as a three space property},
author = {Mahmoud Filali and Jorge Galindo},
journal= {arXiv preprint arXiv:2407.09947},
year = {2025}
}
Comments
The examples in Section 2 have been corrected