On certain classes of Baire-1 functions with applications to Banach space theory

  • R. Haydon
  • E. Odell
  • H. Rosenthal
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1470)


Banach Space Space Theory Basic Sequence Separable Banach Space Spreading Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Andrew, Spreading basic sequences and subspaces of James’ quasi-reflexive space, Math. Scand. 48 (1981), 109–118.MathSciNetzbMATHGoogle Scholar
  2. 2.
    P. Azimi and J.N. Hagler, Examples of hereditarily l 1 Banach spaces failing the Schur property, Pacific J. Math. 122 (1986), 287–297.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    R. Baire, Sur les Fonctions des Variables Réelles, Ann. di Mat. 3 (1899), 1–123.CrossRefzbMATHGoogle Scholar
  4. 4.
    B. Beauzamy and J.-T. Lapresté, Modèles étalés des espaces de Banach, Travaux en Cours, Hermann, Paris (1984).Google Scholar
  5. 5.
    S. Bellenot, More quasi-reflexive subspaces, Proc. AMS 101 (1987), 693–696.MathSciNetzbMATHGoogle Scholar
  6. 6.
    S. Bellenot, R. Haydon and E. Odell, Quasi-reflexive and tree spaces constructed in the spirit of R.C. James, Contemporary Math. 85 (1989), 19–43.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    C. Bessaga and A. Pelczyński, On bases and unconditional convergence of series in Banach spaces, Stud. Math. 17 (1958), 151–164.MathSciNetzbMATHGoogle Scholar
  8. 8.
    J. Bourgain, On convergent sequences of continuous functions, Bull. Soc. Math. Bel. 32 (1980), 235–249.MathSciNetzbMATHGoogle Scholar
  9. 9.
    J. Bourgain, Remarks on the double dual of a Banach space, Bull. Soc. Math. Bel. 32 (1980), 171–178.MathSciNetzbMATHGoogle Scholar
  10. 10.
    J. Bourgain, unpublished notes.Google Scholar
  11. 11.
    P.G. Casazza and T.J. Shura, Tsirelson’s Space, Springer-Verlage Lecture Notes in Mathematics, 1363 (1989).Google Scholar
  12. 12.
    W.J. Davis, T. Figiel, W.B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311–327.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    J. Elton, Extremely weakly unconditionally convergent series, Israel J. Math. 40 (1981), 255–258.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    G.A. Edgar and R.F. Wheeler, Topological properties of Banach spaces, Pacific J. Math. 115 (1984), 317–350.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    C. Finet, Subspaces of Asplund Banach spaces with the point of continuity property, Israel J. Math. 60 (1987), 191–198.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    V. Fonf, One property of Lindenstrauss-Phelps spaces, Funct. Anal. Appl. (English trans.) 13 (1979), 66–67.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    T. Figiel and W.B. Johnson, A uniformly convex Banach space which contains no l p, Comp. Math. 29 (1974), 179–190.MathSciNetzbMATHGoogle Scholar
  18. 18.
    N. Ghoussoub and B. Maurey, G δ-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), 72–97.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    _____, G δ-embeddings in Hilbert space II, J. Funct. Anal. 78 (1998), 271–305.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    _____, H δ-embeddings in Hilbert space and optimization on G δ sets, Memoirs Amer. Math. Soc. 62 (1986), number 349.Google Scholar
  21. 21.
    _____, A non-linear method for constructing certain basic sequences in Banach spaces, Illinois J. Math. 34 (1990), 607–613.MathSciNetzbMATHGoogle Scholar
  22. 22.
    N. Ghoussoub, G. Godefroy, B. Maurey and W. Schachermayer, Some topological and geometrical structures in Banach spaces, Mem. Amer. Math. Soc. 378 (1987).Google Scholar
  23. 23.
    F. Hausdorff, “Set Theory”, Chelsea, New York (1962).zbMATHGoogle Scholar
  24. 24.
    R. Haydon and B. Maurey, On Banach spaces with strongly separable types, J. London Math. Soc. 33 (1986), 484–498.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    A.S. Kechris and A. Louveau, A classification of Baire class 1 functions, Trans. A.M.S. 318 (1990), 209–236.MathSciNetzbMATHGoogle Scholar
  26. 26.
    J.L. Krivine and B. Maurey, Espaces de Banach stables, Israel J. Math. 39 (1981), 273–295.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    J. Lindenstrauss and L. Tzafriri, “Classical Banach spaces”, Springer-Verlag Lecture Notes in Math. 338, Berlin (1973).Google Scholar
  28. 28.
    _____, “Classical Banach spaces II”, Springer-Verlag, Berlin (1977).CrossRefzbMATHGoogle Scholar
  29. 29.
    A.A. Milutin, Isomorphisms of spaces of continuous functions on compacta of power continuum, Tieoria Funct. (1966), 150–166 (Russian).Google Scholar
  30. 30.
    S. Mazurkiewicz and W. Sierpinski, Contribution à la topologie des ensembles dé nombrales, Fund. Math. 1 (1920), 17–27.zbMATHGoogle Scholar
  31. 31.
    A. Pełczyński, A note on the paper of I. Singer “Basic sequences and reflexivity of Banach spaces”, Studia Math. 21 (1962), 371–374.MathSciNetzbMATHGoogle Scholar
  32. 32.
    E. Odell, A nonseparable Banach space not containing a subsymmetric basic sequence, Israel J. Math. 52 (1985), 97–109.MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    _____, Remarks on the separable dual problem, Proceedings of Research Workshop on Banach Space Theory (ed. by B.-L. Lin), The University of Iowa (1981), 129–138.Google Scholar
  34. 34.
    _____, A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing l 1, Comp. Math. 41 (1980), 287–295.MathSciNetzbMATHGoogle Scholar
  35. 35.
    E. Odell and H. Rosenthal, A double-dual characterization of separable Banach spaces not containing l 1, Israel J. Math. 20 (1975), 375–384.MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    H. Rosenthal, A characterization of Banach spaces containing l 1, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413.MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    _____, Weak*-Polish Banach spaces, J. Funct. Anal. 76 (1988), 267–316.MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    _____, Some remarks concerning unconditional basic sequences, Longhorn Notes, University of Texas, (1982–83), 15–48.Google Scholar
  39. 39.
    A. Sersouri, A note on the Lavrientiev index for the quasi-reflexive Banach spaces, Contemporary Math. 85 (1989), 497–508.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • R. Haydon
    • 1
  • E. Odell
    • 2
  • H. Rosenthal
    • 2
  1. 1.Brasenose CollegeOxfordEngland
  2. 2.The University of Texas at AustinAustinU.S.A.

Personalised recommendations