The symmetric Radon-Nikodỳm property for tensor norms

• Autores: Carando, D.; Galicer, D.
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: J. Math. Anal. Appl. 2011;375(2):553-565
• Materia: Metric theory of tensor products; Polynomial ideals; Radon-Nikodỳm property
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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.
Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Galicer, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.