A note on polynomial characterizations of asplund spaces
DOI:
https://doi.org/10.4067/S0716-09172005000100002Abstract
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.
References
[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 (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.
[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.
Published
2017-04-20
How to Cite
[1]
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.
Issue
Section
Artículos
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
