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

Abstract

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