WEAK HOLOMORPHIC CONVERGENCE AND BOUNDING SETS IN BANACH SPACES By

We show that weak holomorphic convergence and norm convergence coincide for sequences in a Banach space E if and only if every bounding subset of E is relatively compact. Introduction Let H(E) denote the vector space of all complex-valued holomorphic functions on a complex Banach space E. Following Petunin and Savkin [18] we say that a sequence (xn) in E is… CONTINUE READING