Carácter topológico de Isomorfismo del Borel

Abstract

Let E be a DFN space, E' its strong topological dual, H(E) and H(E') the corresponding spaces of holomorphic functions from E and E' into endowed with the respective compact-open topologies and Exp E' the vector subspace of H(E') consisting of the entire functions of exponential type on E'. In this article we endow Exp E' with a vector space topology and show that Borel´s Transformation is an isomorphism between the topological vector spaces h(E') (strong topological dual of H(E)) and Exp E'.