Weak amenability of weighted measure algebras and their second duals

2022/10/08 by Mehdipour, M. J., Rejali, A.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.04075

Abstract

In this paper, we study the weak amenability of weighted measure algebras and prove that M(G, ω) is weakly amenable if and only if G is discrete and every bounded quasi-additive function is inner. We also study the weak amenability of L¹(G, ω)^** and M(G, ω)^** and show that the weak amenability of theses Banach algebras are equivalent to finiteness of G. This gives an answer to the question concerning weak amenability of L¹(G, ω)^** and M(G, ω)^**.

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