Duality in Spaces of Nuclear and Integral Polynomials

Abstract

We study the spaces of nuclear and integral (vector-valued) polynomials and their duals. We prove that, if E is Asplund, PN(nE;F)=PI(nE;F) isometrically, for any Banach space F. We describe PN(nE;F)′ as a subspace of P(nE′;F′) in terms of weak-star continuous polynomials. We show that Pw*(nE′;F)=Pc*(nE′;F), when E has the approximation property.