The approximation property for the predual of weighted spaces of holomorphic mappings on Banach spaces

In this paper, we investigate the approximation property for the predual of the weighted space of holomorphic mappings, where is a countable family of weights defined on a balanced open subset U of a Banach space E. We introduce a locally convex topology on and show that is topologically isomorphic to for a suitably restricted family . As a consequence, certain characterizations of the approximation property for the space are proved.