We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R. J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtain...

Let G be a locally compact group, and let 1 < p < ∞. In this paper we investigate the injectivity of the left L1(G)-module Lp(G). We define a family of amenability type conditions called (p, q)-amenability, for any 1 ≤ p ≤ q. For a general locally compact group G we show if Lp(G) is injective, then G must be (p, p)-amenable. For a discrete group G we prove that l p(G) is injective if and only i...

The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras in terms of left Banach -modules. It also offers an application of this result to some Lau algebras related to a locally compact group G, such as the Eymard-Fourier algebra A(G), the Fourier-Stieltjes al...