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

摘要

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 HV_0(U_X, E)) and HW(U_Y, F) (or HW_0(U_Y, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings φ: U_Y → U_X and ψ: U_Y → B(E, F) which generate weighted composition operators between these weighted spaces.