On the cohomology of Banach A∞-module over admissible Banach A∞-algebra

In this paper we are concerned with Banach A∞-module M over admissible Banach A∞-algebra A. We give some properties of admissible modules and algebras. We study the cohomology of the complex C∞(A, M). We show that the vanishing of cohomology of this complex in certain dimensions implies to the existence of the A∞-module structure.