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 $\ell _1$.References
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Additional Information
- Daniel Carando
- Affiliation: Departamento de Economía y Matemática, Universidad de San Andrés, Vito Dumas 284, (1644) Victoria, Argentina
- MR Author ID: 621813
- ORCID: 0000-0002-5519-8697
- Email: daniel@udesa.edu.ar
- Ignacio Zalduendo
- Affiliation: Departamento de Economía y Matemática, Universidad de San Andrés, Vito Dumas 284, (1644) Victoria, Argentina
- MR Author ID: 186385
- Email: nacho@udesa.edu.ar
- Received by editor(s): September 5, 1996
- Received by editor(s) in revised form: May 14, 1997
- Communicated by: Theodore W. Gamelin
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 241-250
- MSC (1991): Primary 46G20; Secondary 46B99
- DOI: https://doi.org/10.1090/S0002-9939-99-04485-8
- MathSciNet review: 1458865