Artículo

Este artículo es de Acceso Abierto y puede ser descargado en su versión final desde nuestro repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product ⊗s, μ n X, for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X. © 2008 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Atomic decompositions for tensor products and polynomial spaces
Autor:Carando, D.; Lassalle, S.
Filiación:Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Atomic decompositions; Homogeneous polynomials; Polynomial ideals; Symmetric tensor norms; Tensor products
Año:2008
Volumen:347
Número:1
Página de inicio:243
Página de fin:254
DOI: http://dx.doi.org/10.1016/j.jmaa.2008.05.051
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_v347_n1_p243_Carando.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v347_n1_p243_Carando

Referencias:

  • Alencar, R., On reflexivity and basis for P (m E) (1985) Proc. Roy. Irish Acad. Sect. A, 85 (2), pp. 131-138
  • Aron, R.M., Hervés, C., Valdivia, M., Weakly continuous mappings on Banach spaces (1983) J. Funct. Anal., 52 (2), pp. 189-204
  • Aron, R.M., Prolla, J.B., Polynomial approximation of differentiable functions on Banach spaces (1980) J. Reine Angew. Math., 313, pp. 195-216
  • Aron, R.M., Schottenloher, M., Compact holomorphic mappings on Banach spaces and the approximation property (1976) J. Funct. Anal., 21, pp. 7-30
  • Blasco, F., Complementation in spaces of symmetric tensor products and polynomials (1997) Studia Math., 123 (2), pp. 165-173
  • Boyd, C., Ryan, R., Geometric theory of spaces of integral polynomials and symmetric tensor products (2001) J. Funct. Anal., 179 (1), pp. 18-42
  • Carando, D., Dimant, V., Duality in spaces of nuclear and integral polynomials (2000) J. Math. Anal. Appl., 241 (1), pp. 107-121
  • Carando, D., Dimant, V., Santiago, M., Coherent sequences of polynomial ideals on Banach spaces (2007) J. Math. Anal. Appl., 336 (2), pp. 1324-1340
  • Daniel Carando, Silvia Lassalle, Duality, reflexivity and atomic decompositions for Banach spaces, preprint; Casazza, P., Han, D., Larson, D., Frames for Banach spaces (1999) Contemp. Math., 247, pp. 149-182. , The Functional and Harmonic Analysis of Wavelets and Frames. San Antonio, TX, 1999, Amer. Math. Soc., Providence, RI
  • Christensen, O., Heil, C., Perturbations of Banach frames and atomic decompositions (1997) Math. Nachr., 185, pp. 33-47
  • Defant, A., Díaz, J.C., García, D., Maestre, M., Unconditional basis and Gordon-Lewis constants for spaces of polynomials (2001) J. Funct. Anal., 181 (1), pp. 119-145
  • Defant, A., Floret, K., (1993) Tensor Norms and Operator Ideals, , North-Holland, Amsterdam
  • Dimant, V., Dineen, S., Banach subspaces of spaces of holomorphic functions and related topics (1998) Math. Scand., 83 (1), pp. 142-160
  • Dimant, V., Zalduendo, I., Bases in spaces of multilinear forms over Banach spaces (1996) J. Math. Anal. Appl., 200 (3), pp. 548-566
  • Dineen, S., Complex Analysis on Infinite Dimensional Spaces (1999) Monogr. Math., , Springer-Verlag
  • Dineen, S., Holomorphy types on Banach space (1971) Studia Math., 39, pp. 241-288
  • Floret, K., Natural norms on symmetric tensor products of normed spaces (1999) Note Mat., 17, pp. 153-188
  • Floret, K., Minimal ideals of n-homogeneous polynomials on Banach spaces (2001) Results Math., 39 (3-4), pp. 201-217
  • Gelbaum, B.R., Gil de Lamadrid, J., Bases of tensor products of Banach spaces (1961) Pacific J. Math., 11, pp. 1281-1286
  • Gröchenig, K., Describing functions: Atomic decompositions versus frames (1991) Monatsh. Math., 112 (1), pp. 1-42
  • Grecu, B., Ryan, R., Schauder bases for symmetric tensor products (2005) Publ. Res. Inst. Math. Sci., 41 (2), pp. 459-469
  • Lindenstrauss, J., Tzafriri, L., (1977) Classical Banach Spaces I and II, , Springer
  • Mujica, J., Complex Analysis in Banach Spaces (1986) Math. Stud., 120. , North-Holland, Amsterdam
  • Pelczyński, A., Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis (1971) Studia Math., 40, pp. 239-243
  • Raymond Ryan, Applications of topological tensor products to infinite dimensional holomorphy, PhD thesis, University College, Dublin, 1980; Ryan, R., The Dunford-Pettis property and projective tensor products (1987) Bull. Pol. Acad. Sci. Math., 35 (11-12), pp. 785-792

Citas:

---------- APA ----------
Carando, D. & Lassalle, S. (2008) . Atomic decompositions for tensor products and polynomial spaces. Journal of Mathematical Analysis and Applications, 347(1), 243-254.
http://dx.doi.org/10.1016/j.jmaa.2008.05.051
---------- CHICAGO ----------
Carando, D., Lassalle, S. "Atomic decompositions for tensor products and polynomial spaces" . Journal of Mathematical Analysis and Applications 347, no. 1 (2008) : 243-254.
http://dx.doi.org/10.1016/j.jmaa.2008.05.051
---------- MLA ----------
Carando, D., Lassalle, S. "Atomic decompositions for tensor products and polynomial spaces" . Journal of Mathematical Analysis and Applications, vol. 347, no. 1, 2008, pp. 243-254.
http://dx.doi.org/10.1016/j.jmaa.2008.05.051
---------- VANCOUVER ----------
Carando, D., Lassalle, S. Atomic decompositions for tensor products and polynomial spaces. J. Math. Anal. Appl. 2008;347(1):243-254.
http://dx.doi.org/10.1016/j.jmaa.2008.05.051