Isomorphisms between spaces of holomorphic mappings on Banach spaces

Abstract

Let and be Banach spaces. Our objective in this work is to find conditions under which, whenever the topological dual spaces and are isomorphic, the spaces of holomorphic mappings of bounded type on and are isomorphic as well. We also examine the corresponding problem for the spaces of holomorphic mappings of a certain type, for instance nuclear bounded type, compact bounded type or weakly compact bounded type.