Strong pseudo-amenability of some Banach algebras

2018/02/06 by Sahami, Amir
#20M18 (Secondary) #43A20 (Primary) #46H05 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1802.02012

Abstract

In this paper we introduce a new notion of strong pseudo-amenability for Banach algebras. We study strong pseudo-amenability of some Matrix algebras. Using this tool, we characterize strong pseudo-amenability of ℓ¹(S), provided that S is a uniformly locally finite semigroup. As an application we show that for a Brandt semigroup S=M⁰(G,I), ℓ¹(S) is strong pseudo-amenable if and only if G is amenable and I is finite. We give some examples to show the differences of strong pseudo-amenability and other classical notions of amenability.

Related

• On pseudo-amenability of Beurling algebras
• Module Pseudo-amenability of Banach algebras
• Symmetrically pseudo-amenable Banach algebras
• Strong pseudo-Connes amenability of dual Banach algebras
• Generalized notion of amenability for a class of matrix algebras