φ-contractibility of some classes of Banach function algebras

Abstract

In this paper, we study ϕ-contractibility of natural Banach function algebras on a compact Hausdorff space. As a consequence, we characterize ϕ-contractibility of the Lipschitz algebra Lip(X, d α ), for a compact metric space (X, d). We also characterize ϕ-contractibility of certain subalgebras of Lipschitz functions including rational Lipschitz algebras, analytic Lipschitz algebras and differentiable Lipschitz algebras.

Generalized notions of module character amenability

“…Hence ℓ 1 (S) is module amenable by [1, Theorem 3.1] and thus it is module character amenable. But if the index set Γ is infinite, then ℓ 1 (S) is not character amenable [12,Corollary 2.7].…”