Proyecciones
Vol. 24, No 1, pp. 13-20, May 2005.
Universidad Católica del Norte
Antofagasta - Chile

A NOTE ON POLYNOMIAL CHARACTERIZATIONS OF ASPLUND SPACES

GERALDO BOTELHO*
Universidade Federal de Uberlândia, Brasil.

and

DANIEL M. PELLEGRINO
Universidade Federal de Campina Grande, Brasil.

Correspondencia a :

ABSTRACT

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. Gutierrez.

2000 Mathematics Subject Classification. Primary: 46G25; Secondary: 47B10.

References

[1] R. Alencar. Multilinear mappings of nuclear and integral type, Proc. Amer. Math. Soc. 94 (1985), 33-38.        [ Links ]

[2] R. Alencar. On reflexivity and basis for P(mE), Proc. Roy. Irish Acad. Sect. A 85 (1985), 131-138.        [ Links ]

[3] R. Alencar and M. Matos. Some classes of multilinear mappings between Banach spaces, Publ. Dep. Analisis Mat. Univ. Complut. Madrid 12 (1989).        [ Links ]

[4] C. Boyd and R. Ryan. Geometric theory of spaces of integral polynomials and symmetric tensor products, J. Funct. Anal. 179 (2001), 18-42.        [ Links ]

[5] D. Carando and V. Dimant. Duality in spaces of nuclear and integral polynomials, J. Math. Anal. Appl. 241 (2000), 107-121.        [ Links ]

[6] R. Cilia and J. Gutiérrez. Polynomial characterization of Asplund spaces, to appear in Bull. Belg. Math. Soc. Simon Stevin.        [ Links ]

[7] J. Diestel and J. J. Uhl. Vector Measures, Amer. Math. Soc. Math. Surveys 15, Providence, 1979.        [ Links ]

[8] S. Dineen. Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London, 1999.        [ Links ]

[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.        [ Links ]

Received : June 2004. Accepted : December 2004

The authors were partially supported by Instituto do Milênio, IMPA. The second named author was partially supported by CNPq and Fundacâo de Amparoá Pesquisa-FAPESQ.

Geraldo Botelho
Faculdade de Matemática
Univ. Federal de Uberlândia
38.400-902 Uberlândia
Brazil
e-mail: botelho@ufu.br

and

Daniel M. Pellegrino
Departamento de Matemática e Estatística
Univ. Federal de Campina Grande
58.109-970 Campina Grande
Brazil
e-mail: dmp@dme.ufcg.edu.br