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Abstract:

We introduce the symmetric Radon-Nikodỳm property (sRN property) for finitely generated s-tensor norms β of order n and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if β is a projective s-tensor norm with the sRN property, then for every Asplund space E, the canonical mapping {position indicator}~βn,sE'→({position indicator}~β'n,sE)' is a metric surjection. This can be rephrased as the isometric isomorphism Qmin(E)=Q(E) for some polynomial ideal Q. We also relate the sRN property of an s-tensor norm with the Asplund or Radon-Nikodỳm properties of different tensor products. As an application, results concerning the ideal of n-homogeneous extendible polynomials are obtained, as well as a new proof of the well-known isometric isomorphism between nuclear and integral polynomials on Asplund spaces. An analogous study is carried out for full tensor products. © 2010 Elsevier Inc.

Registro:

Documento: Artículo
Título:The symmetric Radon-Nikodỳm property for tensor norms
Autor:Carando, D.; Galicer, D.
Filiación:Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
CONICET, Argentina
Palabras clave:Metric theory of tensor products; Polynomial ideals; Radon-Nikodỳm property
Año:2011
Volumen:375
Número:2
Página de inicio:553
Página de fin:565
DOI: http://dx.doi.org/10.1016/j.jmaa.2010.09.044
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v375_n2_p553_Carando.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v375_n2_p553_Carando

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Citas:

---------- APA ----------
Carando, D. & Galicer, D. (2011) . The symmetric Radon-Nikodỳm property for tensor norms. Journal of Mathematical Analysis and Applications, 375(2), 553-565.
http://dx.doi.org/10.1016/j.jmaa.2010.09.044
---------- CHICAGO ----------
Carando, D., Galicer, D. "The symmetric Radon-Nikodỳm property for tensor norms" . Journal of Mathematical Analysis and Applications 375, no. 2 (2011) : 553-565.
http://dx.doi.org/10.1016/j.jmaa.2010.09.044
---------- MLA ----------
Carando, D., Galicer, D. "The symmetric Radon-Nikodỳm property for tensor norms" . Journal of Mathematical Analysis and Applications, vol. 375, no. 2, 2011, pp. 553-565.
http://dx.doi.org/10.1016/j.jmaa.2010.09.044
---------- VANCOUVER ----------
Carando, D., Galicer, D. The symmetric Radon-Nikodỳm property for tensor norms. J. Math. Anal. Appl. 2011;375(2):553-565.
http://dx.doi.org/10.1016/j.jmaa.2010.09.044