Weighted composition operators between weighted spaces of vector-valued holomorphic functions on Banach spaces

Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let U-X and U-Y be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on U-X and U-Y, respectively. Let HV(U-X, E) (or HV0(U-X, E)) and HW(U-Y, F) (or HW0(U-Y, F)) be the weighted spaces of vector- valued holomorphic functions. In this paper, we investigate the holomorphic mappings phi : U-Y -> U-X and psi : U-Y -> B(E, F) which generate weighted composition operators between these weighted spaces. (C) 2011 Elsevier Inc. All rights reserved.