Weighted composition operators on weighted spaces of vector-valued analytic functions

Let V be an arbitrary system of weights on an open connected subset G of ℂ^N (N≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HV_b (G, E) and HVo (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings ψ:G→B (E) which generate weighted composition operators and invertible weighted composition operators on the spaces HV_b (G, E) and HV₀ (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.