On the norm of products of polynomials on ultraproducts of Banach spaces
The purpose of this article is to study the problem of finding sharp lower bounds for the norm of the product of polynomials in the ultraproducts of Banach spaces [Formula: see text]. We show that, under certain hypotheses, there is a strong relation between this problem and the same problem for the...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Academic Press Inc.
2014
|
| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | The purpose of this article is to study the problem of finding sharp lower bounds for the norm of the product of polynomials in the ultraproducts of Banach spaces [Formula: see text]. We show that, under certain hypotheses, there is a strong relation between this problem and the same problem for the spaces Xi. © 2015 Elsevier Inc. All rights reserved. |
|---|---|
| Bibliografía: | Arias-de-Reyna, R.M.J., Gaussian variables, polynomials and permanents (1998) Linear Algebra Appl, 285, pp. 107-114 Aron, R.M., Berner, P.D., A Hahn-Banach extension theorem for analytic mapping (1978) Bull. Soc. Math. France, 106, pp. 3-24 Benítez, C., Sarantopoulos, Y., Tonge, A., Lower bounds for norms of products of polynomials (1998) Math. Proc. Cambridge Philos. Soc, 124, pp. 395-408 Carando, D., Pinasco y, D., Rodríguez, J.T., Lower bounds for norms of products of polynomials on Lpspaces (2013) Studia Math, 214, pp. 157-166 Davie, A.M., Gamelin, T.W., A theorem on polynomial-star approximation (1989) Proc. Amer. Math. Soc, 106, pp. 351-356 Dean, D.W., The equation L(E, X**) =L(E, X)** and the principle of local reflexivity (1973) Proc. Amer. Math. Soc, 40, pp. 146-148 Heinrich, S., Ultraproducts in Banach space theory (1980) J. Reine Angew. Math, 313, pp. 72-104 Lindström, M., Ryan, R.A., Applications of ultraproducts to infinite dimensional holomorphy (1992) Math. Scand, 71, pp. 229-242 Pelłczyński, A., Rosenthal, H., Localization techniques in Lpspaces (1975) Studia Math, 52, pp. 265-289 Pinasco, D., Lower bounds for norms of products of polynomials via Bombieri inequality (2012) Trans. Amer. Math. Soc, 364, pp. 3993-4010 Zalduendo, I., Extending polynomials on Banach spaces-a survey (2005) Rev. Un. Mat. Argentina, 46, pp. 45-72 |
| ISSN: | 0022247X |
| DOI: | 10.1016/j.jmaa.2015.02.054 |