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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Hahn-Banach theorem for integral polynomials


Authors: Daniel Carando and 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 $S$ 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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Additional Information

Daniel Carando
Affiliation: Departamento de Economía y Matemática, Universidad de San Andrés, Vito Dumas 284, (1644) Victoria, Argentina
Email: daniel@udesa.edu.ar

Ignacio Zalduendo
Affiliation: Departamento de Economía y Matemática, Universidad de San Andrés, Vito Dumas 284, (1644) Victoria, Argentina
Email: nacho@udesa.edu.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04485-8
PII: S 0002-9939(99)04485-8
Keywords: Extension of polynomials, containment of $\ell_1$
Received by editor(s): September 5, 1996
Received by editor(s) in revised form: May 14, 1997
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society



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