Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A Hahn-Banach theorem for integral polynomials

Author(s): Daniel Carando; Ignacio Zalduendo
Journal: Proc. Amer. Math. Soc. 127 (1999), 241-250.
MSC (1991): Primary 46G20; Secondary 46B99
MathSciNet review: 1458865
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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 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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