APPROXIMATE AMENABILITY AND A VARIANT OF CONTINUOUS HOCHSCHILD COHOMOLOGY

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 [18], are studied, and a previous result of the author [17] on Lipschitz algebras over compact metric spaces is improved.