Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

Abstract

Abstract Every weakly compact composition operator between weighted Banach spaces 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 are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.