SpringerLink
Log in

On C(K) Grothendieck spaces

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

Using the theory of bounded linear operators, several characterizations of C(K) Grothendieck spaces are given.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bombal F.,Medidas vectoriales y espacios de funciones continuas, Publicaciones del Departamento de Ánalisis Matemático. Facultad de Matemáticas, Universidad Complutense, Madrid, (1984).

    Google Scholar 

  2. Bombal F., Villanueva I.,On the Dunford-Pettis Property of the tensor product of C(K) spaces, Proc. Amer. Math. Soc.,129 5 (2000), 1359–1363.

    Article  MathSciNet  Google Scholar 

  3. Bourgain J.,New Banach spaces properties of the disc algebra and H ∞, Acta Math.,152 (1984), 1–48.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bourgain J.,On the Dunford-Pettis Property, Proc. Amer. Math. Soc.,81 (1981), 265–272.

    Article  MathSciNet  MATH  Google Scholar 

  5. Cembranos P., C(K, E) contains a complemented copy of c0, Proc. AMS,91 (1984), 556–558.

    Article  MathSciNet  MATH  Google Scholar 

  6. Díaz S.,Grothendieck’s Property in L P (X, μ), Glasgow Math. J.,37 (1995), 379–382.

    Article  MathSciNet  MATH  Google Scholar 

  7. Diestel J.,A survey of results related to the Dunford-Pettis Property. Contemporary Math,2 (1980), 15–60.

    MathSciNet  Google Scholar 

  8. Diestel J.,Grothendieck Spaces and Vector Measures, in Vector and Operator Valued Measures and Applications, Proc. Sympos. Snowbird Resort, Alta, Utah, 1972; Academic Press, (1973), 97–108.

  9. Diestel J.,Sequences and Series in Banach Spaces, Graduate Texts in Mathematics.,92 (1984), Springer Verlag.

  10. Diestel J., J. Fourie, J. Swart,The Projective Tensor Product I, Contemporary Mathematics,321 (2003).

  11. Diestel J., Uhl J. J.,Vector Measures, Math. Surveys Amer. Math. Soc.,15 (1977).

  12. Domański P., Lindström M.,Grothendieck spaces and duals of injective tensor products, Bull. London Math. Soc.,28 (1996), 617–626.

    Article  MathSciNet  MATH  Google Scholar 

  13. Gelbaum B. R., Gil de Lamadrid J.,Bases of tensor product of Banach Spaces, Pacific J. Math.,11 (1961), 1281–1286.

    MathSciNet  MATH  Google Scholar 

  14. Grothendieck A.,Sur les applications linéaires faiblement compactes d’espaces du type C(K), Canadian J. Math.,5 (1953), 129–173.

    MathSciNet  MATH  Google Scholar 

  15. Habala P., Hajek P., Zizler V.,Introduction to Banach spaces I, II, Matfyspress, Prague, 1996.

    MATH  Google Scholar 

  16. Johnson W. B.,No infinite dimensional P space admits a Markusevich basis, Proc. Amer. Math. Soc.,26 (1970), 467–468.

    Article  MathSciNet  MATH  Google Scholar 

  17. Leung D.,Uniform convergence of operators and Grothendieck spaces with the Dunford-Pettis Property, Math. Z.,197 (1988), 21–32.

    Article  MathSciNet  MATH  Google Scholar 

  18. Lotz H. P.,Uniform convergence in L ∞ and similar spaces, Math. Z.,190 (1985), 207–220.

    Article  MathSciNet  MATH  Google Scholar 

  19. Meyer-Nieberg P.,Banach Lattices, Springer Verlag, Berlin, 1991.

    MATH  Google Scholar 

  20. van Neerven J. M. A. M.,A converse of Lotz’s theorem on uniformly continuous semigroups, Proc. Amer. Math. Soc.,116, 2 (1992), 525–527.

    Article  MathSciNet  MATH  Google Scholar 

  21. Schaefer H. H.,Banach lattices and positive operators, Springer Verlag, Berlin, 1974.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas Facultad de Ciencias, Universidad de Los Andes, Mérida, Venezuela

    Diómedes Bárcenas

  2. Departamento de Matemáticas Facultad de Ciencias, Universidad Central de Venezuela, Caracas, Venezuela

    Luis Gerardo Mármol

Authors
  1. Diómedes Bárcenas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luis Gerardo Mármol
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Diómedes Bárcenas.

Additional information

Supported by CDCH of ULA under project 1123-02-05-B 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bárcenas, D., Mármol, L.G. On C(K) Grothendieck spaces. Rend. Circ. Mat. Palermo 54, 209–216 (2005). https://doi.org/10.1007/BF02874635

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02874635

Math Subject Classification

Key words and phases

Search

Navigation