Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions

Abstract

Every weakly compact composition operator between weighted Banach spaces H∞v of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space H∞v are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.