Regularity and amenability of weighted Banach algebras and their second dual on locally compact groups

2021/12/25 by Ali Rejali, Rejali, Ali, M. J. Mehdipour +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.2112.13286

arxiv created 2021/12/25 · openalex publication_date 2021/12/25 · arxiv updated 2021/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ω be a weight function on a locally compact group G mand let M_* (G, ω) be the subspace of M(G , ω)^* consisting of all functionals that vanish at infinity. In this paper, we first investigate the Arens regularity of M_* (G, ω)^* and show that M_* (G, ω)^* is Arnes regular if and only if G is finite or ω is zero cluster. This result is an answer to the question posed and it improves some well-known results. We also give necessary and sufficient criteria for the weight function spaces Wap(G , 1/ ω) and Wap(G , 1/ ω) to be equal to C_b (G , 1/ ω) . We prove that for non-compact group G, the Banach algebra M_* (G, ω)^* is Arnes regular if and only if Wap(G , 1/ ω) = C_b (G , 1/ ω) . We then investigate amenability of M_* (G, ω)^* and prove that M_* (G, ω)^* is amenable and Arnes regular if and only if G is finite.

Cited by

• Jordan Left α-centralizers on Algebras with Applications to Group Algebras

Related

• Extreme non-Arens regularity of the group algebra
• Weak amenability of weighted group algebras
• Weighted group algebras
• Weighted L^p-spaces on nilpotent, locally compact groups
• Amenability for dual Banach algebras