Preduals of Spaces of Vector-Valued Holomorphic Functions

Abstract

For U a balanced open subset of a Frechet space E and F a dual-Banach space we introduce the topology τγ on the space \(H\left( {U,F} \right)\) of holomorphic functions from U into F. This topology allows us to construct a predual for \(\left( {H\left( {U,F} \right),\tau \delta } \right)\) 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.