A note on a question of Garth Dales: Arens regularity as a three space property

2024/07/13 by Mahmoud Filali, Filali, Mahmoud, Jorge Galindo +1
Mathematics · #22D15 #43A46 #43A60 #47C15 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2407.09947

openalex publication_date 2024/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Garth Dales asked whether a Banach algebra A having an Arens regular closed ideal J with Arens regular quotient A/J 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.

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