Pointwise amenability for dual Banach algebras

2017/06/21 by Shakeri, Mannane, Mahmoodi, Amin
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1706.07088

Abstract

We shall develop two notions of pointwise amenability, namely pointwise Connes amenability and pointwise w^*-approximate Connes amenability, for dual Banach algebras which take the w^*-topology into account. We shall study these concepts for the Banach sequence algebras ℓ¹(ω) and the weighted semigroup algebras ℓ¹(ℕ_\wedge,ω). For a weight ω on a discrete semigroup S, we shall investigate pointwise amenability/Connes amenability of ℓ¹(S,ω) in terms of diagonals.

Related

• Weakly Connes amenable dual Banach algebras
• Approximate Connes-amenability of dual Banach algebras
• Strong pseudo-Connes amenability of dual Banach algebras
• Pointwise amenable, non-amenable Banach algebras
• Johnson pseudo-Connes amenability of dual Banach algebras