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

Abstract

Let $A(D)$ denote the disk algebra and$W_{\psi ,\varphi }$ be weighted composition operator on $A(D)$.In this paper we obtain a condition on $\psi$ and $\varphi$ for$W_{\psi ,\varphi }$ to exhibit extremal non-compactness. As aconsequence we show that the essential norm of a compositionoperator on $A(D)$ is either 0 or 1.