Artículos de revistas
The symmetric Radon-Nikodým property for tensor norms
Fecha
2010-09-29Registro en:
Carando, Daniel Germán; Galicer, Daniel Eric; The symmetric Radon-Nikodým property for tensor norms; Elsevier; Journal Of Mathematical Analysis And Applications; 375; 2; 29-9-2010; 553-565
0022-247X
Autor
Carando, Daniel Germán
Galicer, Daniel Eric
Resumen
We introduce the symmetric-Radon-Nikodým property (sRN pr operty) 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 prop- erty, then for every Asplund space E , the canonical map e ⊗ n,s β E ′ → e ⊗ n,s β ′ E ′ is a metric surjection. This can be rephrased as the isometric isomorph ism Q min ( E ) = Q ( E ) for certain polynomial ideal Q . We also relate the sRN property of an s-tensor norm with the A splund or Radon-Nikodým properties of different tensor products. S imilar results for full tensor products are also given. As an application, results concern ing the ideal of n -homogeneous extendible polynomials are obtained, as well as a new proof o f the well known isometric isomorphism between nuclear and integral polynomials on As plund spaces.