Isomorphisms between spaces of holomorphic mappings on Banach spaces

Abstract

Let $E$ and $F$ be Banach spaces. Our objective in this work is to find conditions under which, whenever the topological dual spaces $E'$ and $F'$ are isomorphic, the spaces of holomorphic mappings of bounded type on $E$ and $F$ 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.