A Hahn-Banach theorem for integral polynomials

DANIEL CARANDO; IGNACIO ZALDUENDO

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Año: 1999 vol. 127 p. 241 - 250

0002-9939

We study the problem of extendibility of polynomials overBanach spaces: when can a polynomial defined over a Banachspace be extended to a polynomial over any larger Banach space?To this end, we identify all spaces of polynomialsas the topological duals of a space $S$ spanned by evaluations, withHausdorff locally convex topologies. We prove that all integralpolynomials over a Banach space are extendible.Finally, we study the Aron-Berner extension ofintegral polynomials, and give an equivalence fornon-containment of $ell_1$.