Compactness and weak compactness of weighted composition operators on BMOA

Abstract

We show that a weighted composition operator W ψ , φ {W_{\psi ,\varphi }} is compact on BMOA precisely when it is unconditionally converging. As a direct consequence to this result we deduce that all weakly compact or completely continuous weighted composition operators on BMOA are compact. The proof of this result is based on a new simplified function-theoretic characterization of the compactness of weighted composition operators on BMOA.