Approximate amenability and a variant of continuous Hochschild cohomology

Abstract

We study a variant of continuous Hochschild cohomology of a Banach algebra in connection with a higher-dimensional analogue of the approximate amenability of the algebra. Some results on higher-dimensional amenability have natural analogues in our context. Alternating cocycles, due to Johnson \cite {johnson}, are studied, and a previous result of the author B. E. Johnson on Lipschitz algebras over compact metric spaces is improved.