E′ and its relation with vector-valued functions on E

Abstract

We study the relation between different spaces of vector-valued polynomials and analytic functions over dual-isomorphic Banach spaces. Under conditions of regularity on E and F, we show that the spaces of X-valuedn-homogeneous polynomials and analytic functions of bounded type on E and F are isomorphic whenever X is a dual space. Also, we prove that many of the usual subspaces of polynomials and analytic functions on E and F are isomorphic without conditions on the involved spaces.