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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)

Keywords

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.

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References

  1. 1.
    A. Andrew, Spreading basic sequences and subspaces of James’ quasi-reflexive space, Math. Scand. 48 (1981), 109–118.MathSciNetMATHGoogle 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.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    R. Baire, Sur les Fonctions des Variables Réelles, Ann. di Mat. 3 (1899), 1–123.CrossRefMATHGoogle 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.MathSciNetMATHGoogle 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.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    C. Bessaga and A. Pelczyński, On bases and unconditional convergence of series in Banach spaces, Stud. Math. 17 (1958), 151–164.MathSciNetMATHGoogle Scholar
  8. 8.
    J. Bourgain, On convergent sequences of continuous functions, Bull. Soc. Math. Bel. 32 (1980), 235–249.MathSciNetMATHGoogle Scholar
  9. 9.
    J. Bourgain, Remarks on the double dual of a Banach space, Bull. Soc. Math. Bel. 32 (1980), 171–178.MathSciNetMATHGoogle 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    J. Bourgain, unpublished notes.Google Scholar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.MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    J. Elton, Extremely weakly unconditionally convergent series, Israel J. Math. 40 (1981), 255–258.MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    G.A. Edgar and R.F. Wheeler, Topological properties of Banach spaces, Pacific J. Math. 115 (1984), 317–350.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    C. Finet, Subspaces of Asplund Banach spaces with the point of continuity property, Israel J. Math. 60 (1987), 191–198.MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    V. Fonf, One property of Lindenstrauss-Phelps spaces, Funct. Anal. Appl. (English trans.) 13 (1979), 66–67.MathSciNetCrossRefMATHGoogle 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.MathSciNetMATHGoogle Scholar
  18. 18.
    N. Ghoussoub and B. Maurey, G δ-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), 72–97.MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    _____, G δ-embeddings in Hilbert space II, J. Funct. Anal. 78 (1998), 271–305.MathSciNetCrossRefMATHGoogle 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.MathSciNetMATHGoogle 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).MATHGoogle Scholar
  24. 24.
    R. Haydon and B. Maurey, On Banach spaces with strongly separable types, J. London Math. Soc. 33 (1986), 484–498.MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    A.S. Kechris and A. Louveau, A classification of Baire class 1 functions, Trans. A.M.S. 318 (1990), 209–236.MathSciNetMATHGoogle Scholar
  26. 26.
    J.L. Krivine and B. Maurey, Espaces de Banach stables, Israel J. Math. 39 (1981), 273–295.MathSciNetCrossRefMATHGoogle 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).CrossRefMATHGoogle 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.MATHGoogle 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.MathSciNetMATHGoogle Scholar
  32. 32.
    E. Odell, A nonseparable Banach space not containing a subsymmetric basic sequence, Israel J. Math. 52 (1985), 97–109.MathSciNetCrossRefMATHGoogle 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.MathSciNetMATHGoogle 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.MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    H. Rosenthal, A characterization of Banach spaces containing l 1, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413.MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    _____, Weak*-Polish Banach spaces, J. Funct. Anal. 76 (1988), 267–316.MathSciNetCrossRefMATHGoogle 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.MathSciNetCrossRefMATHGoogle 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.

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