On homological notions of Banach algebras related to a character

2014/01/11 by Sahami, A.
#43A20 #46M10 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A07 #Secondary 46H05

paper · doi:10.48550/arxiv.1401.2558

Abstract

In this paper, we countinue our work in \cite11. We show that L¹(G,w) is ϕ₀-biprojective if and only if G is compact, where ϕ₀ is the augmentation character. We introduce the notions of character Johnson amenability and character Johnson contractibility for Banach algebras. We show that ℓ¹(S) is pseudo-amenable if and only if ℓ¹(S) is character Johnson-amenable, provided that S is a uniformly locally finite band semigroup. We give some conditions whether ϕ-biprojectivity (ϕ-biflatness) of ℓ¹(S) implies the finiteness (amenability) of S, respectively.

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