A Hahn-Banach theorem for integral polynomials

Abstract

We study the problem of extendibility of polynomials over Danach spaces: when can a polynomial defined over a Banach space be extended to a polynomial over any larger Banach space? To this end, we identify all spaces of polynomials as the topological duals of a space 5 spanned by evaluations, with Hausdorff locally convex topologies. We prove that all integral polynomials over a Banach space are extendible. Finally, we study the Aron-Berner extension of integral polynomials, and give an equivalence for non-containment of ii. ©1999 American Mathematical Society.