WEIGHTED COMPOSITION OPERATORS ON WEIGHTED SPACES OF VECTOR-VALUED ANALYTIC FUNCTIONS

Abstract

Let V be an arbitrary system of weights on an open connected subset G of and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let (G, E) and (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings and operator-valued analytic mappings which generate weighted composition operators and invertible weighted composition operators on the spaces (G, E) and (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