Preduals of spaces of vector-valued holomorphic functions

For U a balanced open subset of a Frechet space E and F a dual-Banach space we introduce the topology tau(gamma) on the space H(U, F) of holomorphic functions from U into F. This topology allows us to construct a predual for (H(U, F), tau(delta)) which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions.