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Abstract:

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.

Registro:

Documento: Artículo
Título:On the norm of products of polynomials on ultraproducts of Banach spaces
Autor:Rodríguez, J.T.
Filiación:Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
IMAS-CONICET, Argentina
Palabras clave:Banach spaces; Norm inequalities; Polynomials; Ultraproducts
Año:2014
Volumen:427
Número:2
Página de inicio:805
Página de fin:816
DOI: http://dx.doi.org/10.1016/j.jmaa.2015.02.054
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v427_n2_p805_Rodriguez

Referencias:

  • 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

Citas:

---------- APA ----------
(2014) . On the norm of products of polynomials on ultraproducts of Banach spaces. Journal of Mathematical Analysis and Applications, 427(2), 805-816.
http://dx.doi.org/10.1016/j.jmaa.2015.02.054
---------- CHICAGO ----------
Rodríguez, J.T. "On the norm of products of polynomials on ultraproducts of Banach spaces" . Journal of Mathematical Analysis and Applications 427, no. 2 (2014) : 805-816.
http://dx.doi.org/10.1016/j.jmaa.2015.02.054
---------- MLA ----------
Rodríguez, J.T. "On the norm of products of polynomials on ultraproducts of Banach spaces" . Journal of Mathematical Analysis and Applications, vol. 427, no. 2, 2014, pp. 805-816.
http://dx.doi.org/10.1016/j.jmaa.2015.02.054
---------- VANCOUVER ----------
Rodríguez, J.T. On the norm of products of polynomials on ultraproducts of Banach spaces. J. Math. Anal. Appl. 2014;427(2):805-816.
http://dx.doi.org/10.1016/j.jmaa.2015.02.054