Extremal non-compactness of weighted composition operators on the disk algebra

Abstract

Let A(D) denote the disk algebra and Wψ,φ be weighted composition operator on A(D). In this paper we obtain a condition on ψ and φ for Wψ,φ to exhibit extremal non-compactness. As a consequence we show that the essential norm of a composition operator on A(D) is either 0 or 1.