Ir al contenido

Documat


On operator ideals defined by a reflexive Orlicz sequence space

  • López Molina, J. A. [1] Árbol académico ; Rivera, M. J. [1] Árbol académico ; Loaiza, G. [2]
    1. [1] Universidad Politécnica de Valencia

      Universidad Politécnica de Valencia

      Valencia, España

    2. [2] Universidad EAFIT

      Universidad EAFIT

      Colombia

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 25, Nº. 3, 2006, págs. 271-291
  • Idioma: inglés
  • DOI: 10.4067/S0716-09172006000300005
  • Enlaces
  • Resumen
    • Classical theory of tensornorms and operator ideals studies mainly those defined by means of sequence spaces ℓp. Considering Orlicz sequence spaces as natural generalization of ℓp spaces, in a previous paper [12] an Orlicz sequence space was used to define a tensornorm, and characterize minimal and maximal operator ideals associated, by using local techniques. Now, in this paper we give a new characterization of the maximal operator ideal to continue our analysis of some coincidences among such operator ideals. Finally we prove some new metric properties of tensornorm mentioned above.

  • Referencias bibliográficas
    • Citas [1] Aliprantis, C. D., Burkinshaw, O.: Positive operators. Pure and Applied Mathematics 119. Academic Press, Newe York, (1985).
    • [2] Diestel, J. and Uhl, J. J. Jr.: Vector measures. Mathematical Surveys and Monographs. Number 15. American Mathematical Society. U. S....
    • [3] De Grande-De Kimpe, N.: Λ-mappings between locally convex spaces, Indag. Math. 33, pp. 261-274, (1971).
    • [4] Defant, A. and Floret, K.: Tensor norms and operator ideals. North Holland Math. Studies. Amsterdam. (1993).
    • [5] Dubinsky, E. and Ramanujan, M. S.: On M-nuclearity. Mem. Amer. Math. Soc. 128, (1972).
    • [6] Harksen, J.: Tensornormtopologien. Dissertation, Kiel, (1979).
    • [7] Haydon, R., Levy, M., Raynaud, Y.: Randomly normed spaces. Hermann, (1991).
    • [8] Heinrich, S.: Ultraproducts in Banach spaces theory. J. reine angew. Math. 313, pp. 72-104, (1980).
    • [9] Johnson, W. B.: On finite dimensional subspaces of Banach spaces with local unconditional structure. Studia Math. 51, pp. 225-240, (1974).
    • [10] Komura, T., Komura, Y.: Sur les espaces parfaits de suites et leurs généralisations, J. Math. Soc. Japan, 15,3, pp. 319-338, (1963).
    • [11] Lacey, H. E.: The isometric theory of Classical Banach spaces, Springer Verlag. Berlin, Heidelberg, New York, (1974)
    • [12] Loaiza, G., López Molina, J.A., Rivera, M.J.: Characterization of the Maximal Ideal of Operators Associated to the Tensor Norm Defined...
    • [13] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces I and II, Springer Verlang. Belin, Heidelberg, New York, (1977).
    • [14] Lindenstrauss, J., Tzafriri, L.: The uniform approximation property in Orlicz spaces, Israel J. Math. 23, 2, pp. 142-155,(1976).
    • [15] Pelczynski, A., Rosenthal, H. P.: Localization techniques in Lp spaces, Studia Math. 52, pp. 263-289, (1975).
    • [16] Pietsch, a.: Operator Ideals. North Holland Math. Library. Amsterdam, New York. (1980).
    • [17] Rivera, M.J.: On the classes of Lλ, Lλ,g and quasi-LE spaces. Preprint
    • [18] Saphar, P.: Produits tensoriels topologiques et classes d’applications lineaires. Studia Math. 38, pp. 71-100, (1972).
    • [19] Sims, B.: ”Ultra”-techniques in Banach space theory, Queen’s Papers in Pure and Applied Mathematics, 60. Ontario, (1982).
    • [20] Tomasek, S: Projectively generated topologies on tensor products, Comentations Math. Univ. Carolinae, 11, 4 (1970).

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno