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A note on polynomial characterizations of asplund spaces

  • Botelho, Geraldo [1] ; Pellegrino, Daniel M. [2]
    1. [1] Universidade Federal de Uberlândia

      Universidade Federal de Uberlândia

      Brasil

    2. [2] Universidade Federal de Campina Grande

      Universidade Federal de Campina Grande

      Brasil

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 24, Nº. 1, 2005, págs. 13-20
  • Idioma: inglés
  • DOI: 10.4067/S0716-09172005000100002
  • Enlaces
  • Resumen
    • In this note we obtain several characterizations of Asplund spaces by means of ideals of Pietsch integral and nuclear polynomials, extending previous results of R. Alencar and R. Cilia-J. Gutiérrez.

  • Referencias bibliográficas
    • Citas [1] R. Alencar. Multilinear mappings of nuclear and integral type, Proc. Amer. Math. Soc. 94 (1985), 33-38.
    • [2] R. Alencar. On reflexivity and basis for P(mE), Proc. Roy. Irish Acad. Sect. A 85 (1985), 131-138.
    • [3] R. Alencar and M. Matos. Some classes of multilinear mappings between Banach spaces, Publ. Dep. Analisis Mat. Univ. Complut. Madrid 12...
    • [4] C. Boyd and R. Ryan. Geometric theory of spaces of integral polynomials and symmetric tensor products, J. Funct. Anal. 179 (2001), 18-42.
    • [5] D. Carando and V. Dimant. Duality in spaces of nuclear and integral polynomials, J. Math. Anal. Appl. 241 (2000), 107-121.
    • [6] R. Cilia and J. Gutiérrez. Polynomial characterization of Asplund spaces, to appear in Bull. Belg. Math. Soc. Simon Stevin.
    • [7] J. Diestel and J. J. Uhl. Vector Measures, Amer. Math. Soc. Math. Surveys 15, Providence, 1979.
    • [8] S. Dineen. Complex Analysis on Infinite Dimensional Spaces, SpringerVerlag, London, 1999.
    • [9] A. Pietsch. Ideals of multilinear functionals, Proceedings of the Second International Conference on Operator Algebras, Ideals and Their...

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