Weakly continuous holomorphic functions on Banach spaces with a shrinking and unconditional basis

Let E and F be complex Banach spaces, and let U be an open ball in E. We show that if E has a shrinking and unconditional basis, then every holomorphic function f :U →F that is weakly continuous on U-bounded sets is weakly uniformly continuous on U-bounded sets. © 2007 Elsevier Inc. All rights reserved