ϕ-Contractibility of Some Classes of Banach Function Algebras

Abstract

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