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

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References

  1. A. Andrew, Spreading basic sequences and subspaces of James’ quasi-reflexive space, Math. Scand. 48 (1981), 109–118.

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Baire, Sur les Fonctions des Variables Réelles, Ann. di Mat. 3 (1899), 1–123.

    Article  MATH  Google Scholar 

  4. B. Beauzamy and J.-T. Lapresté, Modèles étalés des espaces de Banach, Travaux en Cours, Hermann, Paris (1984).

    Google Scholar 

  5. S. Bellenot, More quasi-reflexive subspaces, Proc. AMS 101 (1987), 693–696.

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  7. C. Bessaga and A. Pelczyński, On bases and unconditional convergence of series in Banach spaces, Stud. Math. 17 (1958), 151–164.

    MathSciNet  MATH  Google Scholar 

  8. J. Bourgain, On convergent sequences of continuous functions, Bull. Soc. Math. Bel. 32 (1980), 235–249.

    MathSciNet  MATH  Google Scholar 

  9. J. Bourgain, Remarks on the double dual of a Banach space, Bull. Soc. Math. Bel. 32 (1980), 171–178.

    MathSciNet  MATH  Google Scholar 

  10. J. Bourgain, unpublished notes.

    Google Scholar 

  11. P.G. Casazza and T.J. Shura, Tsirelson’s Space, Springer-Verlage Lecture Notes in Mathematics, 1363 (1989).

    Google Scholar 

  12. W.J. Davis, T. Figiel, W.B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311–327.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Elton, Extremely weakly unconditionally convergent series, Israel J. Math. 40 (1981), 255–258.

    Article  MathSciNet  MATH  Google Scholar 

  14. G.A. Edgar and R.F. Wheeler, Topological properties of Banach spaces, Pacific J. Math. 115 (1984), 317–350.

    Article  MathSciNet  MATH  Google Scholar 

  15. C. Finet, Subspaces of Asplund Banach spaces with the point of continuity property, Israel J. Math. 60 (1987), 191–198.

    Article  MathSciNet  MATH  Google Scholar 

  16. V. Fonf, One property of Lindenstrauss-Phelps spaces, Funct. Anal. Appl. (English trans.) 13 (1979), 66–67.

    Article  MathSciNet  MATH  Google Scholar 

  17. T. Figiel and W.B. Johnson, A uniformly convex Banach space which contains no l p , Comp. Math. 29 (1974), 179–190.

    MathSciNet  MATH  Google Scholar 

  18. N. Ghoussoub and B. Maurey, G δ-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), 72–97.

    Article  MathSciNet  MATH  Google Scholar 

  19. _____, G δ-embeddings in Hilbert space II, J. Funct. Anal. 78 (1998), 271–305.

    Article  MathSciNet  MATH  Google Scholar 

  20. _____, H δ-embeddings in Hilbert space and optimization on G δ sets, Memoirs Amer. Math. Soc. 62 (1986), number 349.

    Google Scholar 

  21. _____, A non-linear method for constructing certain basic sequences in Banach spaces, Illinois J. Math. 34 (1990), 607–613.

    MathSciNet  MATH  Google Scholar 

  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. F. Hausdorff, “Set Theory”, Chelsea, New York (1962).

    MATH  Google Scholar 

  24. R. Haydon and B. Maurey, On Banach spaces with strongly separable types, J. London Math. Soc. 33 (1986), 484–498.

    Article  MathSciNet  MATH  Google Scholar 

  25. A.S. Kechris and A. Louveau, A classification of Baire class 1 functions, Trans. A.M.S. 318 (1990), 209–236.

    MathSciNet  MATH  Google Scholar 

  26. J.L. Krivine and B. Maurey, Espaces de Banach stables, Israel J. Math. 39 (1981), 273–295.

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Lindenstrauss and L. Tzafriri, “Classical Banach spaces”, Springer-Verlag Lecture Notes in Math. 338, Berlin (1973).

    Google Scholar 

  28. _____, “Classical Banach spaces II”, Springer-Verlag, Berlin (1977).

    Book  MATH  Google Scholar 

  29. A.A. Milutin, Isomorphisms of spaces of continuous functions on compacta of power continuum, Tieoria Funct. (1966), 150–166 (Russian).

    Google Scholar 

  30. S. Mazurkiewicz and W. Sierpinski, Contribution à la topologie des ensembles dé nombrales, Fund. Math. 1 (1920), 17–27.

    MATH  Google Scholar 

  31. A. Pełczyński, A note on the paper of I. Singer “Basic sequences and reflexivity of Banach spaces”, Studia Math. 21 (1962), 371–374.

    MathSciNet  MATH  Google Scholar 

  32. E. Odell, A nonseparable Banach space not containing a subsymmetric basic sequence, Israel J. Math. 52 (1985), 97–109.

    Article  MathSciNet  MATH  Google Scholar 

  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. _____, A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing l 1, Comp. Math. 41 (1980), 287–295.

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  36. H. Rosenthal, A characterization of Banach spaces containing l 1, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413.

    Article  MathSciNet  MATH  Google Scholar 

  37. _____, Weak*-Polish Banach spaces, J. Funct. Anal. 76 (1988), 267–316.

    Article  MathSciNet  MATH  Google Scholar 

  38. _____, Some remarks concerning unconditional basic sequences, Longhorn Notes, University of Texas, (1982–83), 15–48.

    Google Scholar 

  39. A. Sersouri, A note on the Lavrientiev index for the quasi-reflexive Banach spaces, Contemporary Math. 85 (1989), 497–508.

    Article  MathSciNet  MATH  Google Scholar 

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Edward E. Odwell Jr. Haskell P. Rosenthal

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© 1991 Springer-Verlag

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Haydon, R., Odell, E., Rosenthal, H. (1991). On certain classes of Baire-1 functions with applications to Banach space theory. In: Odwell, E.E., Rosenthal, H.P. (eds) Functional Analysis. Lecture Notes in Mathematics, vol 1470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090209

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  • DOI: https://doi.org/10.1007/BFb0090209

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