Multiplication operators and dynamical systems on weighted spaces of vector-valued holomorphic functions on banach spaces

Let U_X be a balanced open subset of a Banach space X. Let V and W be two Nachbin families of weights on U_X. Let B(E, F) be the space of all continuous linear operators from a locally convex Haudorff space E into a locally convex Hausdorff space F. Let HV (U_X, F) and HW (U_X, E) be the weighted locally convex spaces of vector-valued holomorphic functions. In this paper, we investigate the operator-valued maps ψ: U_X → B (E,F) which generate multiplication operators and invertible multiplication operators Mψ on the spaces HV (U_X, F) and HW (U_X, E) for general Nachbin families of weights V and W and for single continuous weights v and w on the open unit ball B_X of a Banach space X. A C₀-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.