Skip to main content
Log in

The alternative Dunford-Pettis property on projective tensor products

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Acosta, M.D., Peralta, A.M.: An alternative Dunford-Pettis property for JB*-triples. Quart. J. Math. Oxford Ser. 52, 391–401 (2001)

    MATH  MathSciNet  Google Scholar 

  2. Becerra Guerrero, J., López Pérez, G., Peralta, A.M., Rodríguez Palacios, A.: Relatively weakly open sets in closed balls of Banach spaces, and real JB*-triples of finite rank. Math. Ann. 330, 45–58 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Becerra Guerrero, J., Peralta, A.M.: The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples, Math. Z. 251, 117–130 (2005)

    MATH  Google Scholar 

  4. Bombal, F., Villanueva, I.: On the Dunford-Pettis property of the tensor product of C(K) spaces. Proc. Amer. Math. Soc. 129(5), 1359–1363 (2001)

    Article  MathSciNet  Google Scholar 

  5. Bunce, L.J., Chu, Ch.-H.: Dual spaces of JB*-triples and the Radon-Nikodým property. Math. Z. 208(2), 327–334 (1991)

    MathSciNet  Google Scholar 

  6. Bunce, L.J., Chu, Ch.-H.: Compact operations, multipliers and Radon-Nikodým property in JB*-triples. Pacific J. Math. 153(2), 249–265 (1992)

    MathSciNet  Google Scholar 

  7. Bunce, L.J., Peralta, A.M.: The alternative Dunford-Pettis property in C*-algebras and von Neumann preduals. Proc. Amer. Math. Soc. 131(4), 1251–1255 (2003)

    Article  MathSciNet  Google Scholar 

  8. Cabello, F., García, R.: The bidual of a tensor product of Banach spaces. To appear in Rev. Mat. Iber.

  9. Cabello, F., Pérez-García, D., Villanueva, I.: Unexpected subspaces of tensor products, preprint 2004

  10. Chu, Ch.-H., Iochum, B.: On the Radon-Nikodým property in Jordan triples, Proc. Amer. Math. Soc. 99(3), 462–464 (1987)

    Article  Google Scholar 

  11. Chu, Ch.-H., Iochum, B.: Complementation of Jordan triples in von Neumann algebras. Proc. Amer. Math. Soc. 108(1), 19–24 (1990)

    Article  MathSciNet  Google Scholar 

  12. Defant, A., Floret, K.: Tensor norms and operator ideals, North-Holland Mathematics Studies, 176. North-Holland Publishing Co., Amsterdam, 1993

  13. Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge Univ. Press, 1995

  14. Dineen, S.: The second dual of a JB*-triple system, In: J. Múgica) (ed.) Complex analysis, functional analysis and approximation theory , pp. 67–69, (North-Holland Math. Stud. 125), North-Holland, Amsterdam-New York, 1986

  15. Freedman, W.: An alternative Dunford-Pettis property. Studia Math. 125, 143–159 (1997)

    MATH  MathSciNet  Google Scholar 

  16. Friedman, Y., Russo, B.: Structure of the predual of a JBW*-triple. J. Reine u. Angew. Math. 356, 67–89 (1985)

    MATH  Google Scholar 

  17. González, M., Gutiérrez, J.: The Dunford-Pettis property on tensor products. Math. Proc. Camb. Phil. Soc. 131, 185–192 (2001)

    Article  MATH  Google Scholar 

  18. Grothendieck, A.: Sur les applications lineaires faiblement compactes d'espaces du type C(K). Canad. J. Math. 5, 129–173 (1953)

    MATH  MathSciNet  Google Scholar 

  19. Horn, G.: Characterization of the predual and ideal structure of a JBW*-triple. Math. Scand. 61(1), 117–133 (1987)

    MathSciNet  Google Scholar 

  20. Kadison, R.V., Ringrose, J.R.: Fundamentals of the theory of operator algebras. Vol. I. Elementary theory. Pure and Applied Mathematics, 100. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983

  21. Kaup, W.: Algebraic Characterization of symmetric complex Banach manifolds.Math. Ann. 228, 39–64 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  22. Kaup, W.: A Riemann Mapping Theorem for bounded symmentric domains in complex Banach spaces. Math. Z. 183, 503–529 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  23. Pełczyński, A., Semadeni, Z.: Spaces of continuous functions. III. Spaces C(Ω ) for Ω without perfect subsets. Studia Math. 18, 211–222 (1959)

    MATH  Google Scholar 

  24. Semadeni, Z.: Banach spaces of continuous functions. Vol. I. Monografie Matematyczne, Tom 55. PWN—Polish Scientific Publishers, Warsaw, 1971

  25. Stegall, C.: Duals of certain spaces with the Dunford-Pettis property. Notices Amer. Math. Soc. 19, A-799 (1972)

    Google Scholar 

  26. Talagrand, M.: La propriété de Dunford-Pettis dans (K, E) et L 1(E). Israel J. Math. 44(4), 317–321 (1983)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Antonio M. Peralta.

Additional information

First author partially supported by I+D MCYT project no. MTM2005-02541, and Junta de Andalucía grant FQM 0199 and second author partially supported by I+D MCYT project no. MTM2004-01308

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peralta, A., Villanueva, I. The alternative Dunford-Pettis property on projective tensor products. Math. Z. 252, 883–897 (2006). https://doi.org/10.1007/s00209-005-0894-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-005-0894-6

Keywords

Navigation