Weak amenability of weighted group algebras

2022/09/17 by Mehdipour, M. J., Rejali, A.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2209.08346

Abstract

In this paper, we study weak amenability of Beurling algebras. To this end, we introduce the notion inner quasi-additive functions and prove that for a locally compact group G, the Banach algebra L¹(G, ω) is weakly amenable if and only if every non-inner quasi-additive function in L^∞(G, 1/ω) is unbounded. This provides an answer to the question concerning weak amenability of L¹(G, ω) and improve some known results in connection with it.

Related

• Non-weakly amenable Beurling algebras
• Weak amenability of commutative Beurling algebras
• Weak amenability of weighted measure algebras and their second duals
• Generalization of Weak Amenability of Banach Algebras
• Approximate weak amenability of certain Banach algebras