EVALUATION FUNCTIONS AND REFLEXIVITY OF BANACH SPACES OF HOLOMORPHIC FUNCTIONS

Abstract

Abstract Let $B(\Omega )$ be a Banach space of holomorphic functions on a bounded connected domain $\Omega $ in ${{\mathbb C}^n}$ . In this paper, we establish a criterion for $B(\Omega )$ to be reflexive via evaluation functions on $B(\Omega )$ , that is, $B(\Omega )$ is reflexive if and only if the evaluation functions span the dual space $(B(\Omega ))^{*} $ .