The bounded approximation property for spaces of holomorphic mappings on infinite dimensional spaces

Abstract

We study the bounded approximation property for spaces of holomorphic functions. We show that if U is a balanced open subset of a Frechet-Schwartz space or (DFM)-space E, then the space R(U) of holomorphic mappings on U, with the compact-open topology, has the bounded approximation property if and only if E has the bounded approximation property.