A Cohomological Property of π-invariant Elements

Abstract

Abstract. Let A be a Banach algebra and π : A −→ L (H) be a continuous representation of A on a separable Hilbert space H with dim H = m. Let π i j be the coordinate functions of π with respect to an orthonormal basis and suppose that for eachIn this paper we prove a link between the existence of left π-invariant elements and the vanishing of certain Hochschild cohomology groups of A. Our results extend an earlier result by Lau on F-algebras and recent results of Kaniuth-Lau-Pym and the second named author in the special case that π : A −→ C is a non-zero character on A.