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 a consequence we show that the essential norm of a composition operator on $A({D})$ is either 0 or 1.

Keywords: Essential norm; composition operator; inner function; extremal non-compactness.

MSC: 47B33

Pages:  19$-$22     

Volume  62 ,  Issue  1 ,  2010