A Hahn-Banach theorem for integral polynomials

Carando, Daniel; Zalduendo, Ignacio

doi:10.1090/S0002-9939-99-04485-8

A Hahn-Banach theorem for integral polynomials
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by Daniel Carando and Ignacio Zalduendo PDF

Proc. Amer. Math. Soc. 127 (1999), 241-250 Request permission

Abstract:

We study the problem of extendibility of polynomials over Banach 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 $S$ 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 $\ell _1$.

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