A note on polynomial characterizations of asplund spaces


  • Geraldo Botelho Universidade Federal de Uberlandia.
  • Daniel M. Pellegrino Universidade Federal de Campina Grande.




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.

Author Biographies

Geraldo Botelho, Universidade Federal de Uberlandia.

Faculdade de Matemática.  

Daniel M. Pellegrino, Universidade Federal de Campina Grande.

Departamento de Matemática e Estatística.


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[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 (1989).

[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 Applications in Theoretical Physics, 185-199, Teubner-Texte, Leipzig, 1983.



How to Cite

G. Botelho and D. M. Pellegrino, “A note on polynomial characterizations of asplund spaces”, Proyecciones (Antofagasta, On line), vol. 24, no. 1, pp. 13-20, Apr. 2017.