Johnson pseudo-contractibility of various classes of Banach algebras

Abstract

The notion of Johnson pseudo-contractibility for Banach algebras is introduced. We investigate this notion for Banach algebras defined on locally compact groups. For a compact metric space $X$ and $\alpha>0$, we show that the Lipschitz algebra $Lip_{\alpha}(X)$ is Johnson pseudo-contractible if and only if $X$ is finite. We give some examples to distinguish our new notion with the classical ones.