On operator ideals defined by a reflexive Orlicz sequence space

  • J. A. López Molina Universidad Politécnica de Valencia.
  • M. J. Rivera Universidad Politécnica de Valencia.
  • G. Loaiza Universidad EAFIT.
Palabras clave: Maximal operator ideals, ultraproducts of spaces, Orlicz spaces, ideales de operadores máximos, ultraproductos de espacios, espacios de Orlicz.


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.

Biografía del autor

J. A. López Molina, Universidad Politécnica de Valencia.
E.T.S. Ingenieros Agrónomos.
M. J. Rivera, Universidad Politécnica de Valencia.
E.T.S. Ingenieros Agrónomos.
G. Loaiza, Universidad EAFIT.
Departamento de Ciencias Básicas.


[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. A. (1977).

[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 by an Orlicz Function. Zeitschrift fur Analysis und ihre Anwendungen (Journal for Analysis and its Applications) 20, no.2, pp. 281-293, (2001).

[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).
Cómo citar
J. López Molina, M. Rivera, y G. Loaiza, On operator ideals defined by a reflexive Orlicz sequence space, PJM, vol. 25, n.º 3, pp. 271-291, may 2017.