Arens regularity of ideals in A(G), A_cb(G) and A_M(G)

2023/02/11 by Brian Forrest, Forrest, Brian, John Sawatzky +3
Mathematics · #46J10 #47L25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 43A07 #Rings, Modules, and Algebras #Secondary: 43A22

paper · pdf · doi:10.48550/arxiv.2302.05699

openalex publication_date 2023/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we look at the question of when various ideals in the Fourier algebra A(G) or its closures A_M(G) and A_cb(G) in, respectively, its multiplier and cb-multiplier algebra are Arens regular. We show that in each case, if a non-zero ideal is Arens regular, then the underlying group G must be discrete. In addition, we show that if an ideal I in A(G) has a bounded approximate identity, then it is Arens regular if and only if it is finite-dimensional.

Related

• Arens regularity and irregularity of ideals in Fourier and group algebras
• A note on a question of Garth Dales: Arens regularity as a three space property
• Approximate Identity and Arens Regularity of Some Banach Algebras
• Arens regularity of the Orlicz Figà-Talamanca Herz Algebra
• Extreme non-Arens regularity of the group algebra