On the Richness of the Set of p’s in Krivine’s Theorem

  • E. Odell
  • Th. Schlumprecht
Part of the Operator Theory Advances and Applications book series (OT, volume 77)


We give examples of two Banach spaces. One Banach space has no spreading model which contains p (1 ≤ p < ∞) or c o. The other space has an unconditional basis for which p (1 ≥ p < ∞) and c o are block finitely represented in all block bases.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BL]
    B. Beauzamy and J.-T. Lapresté, Modèles étalés des espaces de Banach, In “Travaux en Cours”, Hermann, Paris, 1984.Google Scholar
  2. [BS1]
    A. Brunel and L. Sucheston, On J-convexity and some ergodic superproperties of Banach spaces, Trans. Amer. Math. Soc. 204 (1975), 79–90.MathSciNetzbMATHGoogle Scholar
  3. [BS2]
    A. Brunel and L. Sucheston, On B-convex Banach spaces, Math. Systems Th. 7 (1974), 294–299.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [CS]
    P.G. Casazza and T.J. Shura, Tsirelson’s Space, In “Lecture Notes in Mathematics” 1363, Springer-Verlag, 1989.Google Scholar
  5. [FJ]
    T. Figiel and W.B. Johnson, A uniformly convex Banach space which contains no l p, Comp. Math. 29 (1974), 179–190.MathSciNetzbMATHGoogle Scholar
  6. [G]
    W.T. Gowers, A space not containing c o, 1 or a reflexive subspace, preprint.Google Scholar
  7. [GM]
    W.T. Gowers and B. Maurey, The unconditional basic sequence problem, Journal of AMS 6 (1993), 851–874.MathSciNetzbMATHGoogle Scholar
  8. [J]
    R.C. James, Uniformly nonsquare Banach spaces, Ann. of Math. 80 (1964), 542–550.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [K]
    J.L. Krivine, Sous espaces de dimension finie des espaces de Banach réticulés, Ann. of Math. 104 (1976), 1–29.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [L]
    H. Lemberg, Nouvelle démonstration d’un théorème de J.L. Krivine sur la finie représentation de p dans un espace de Banach, Israel J. Math. 39 (1981), 341–348.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [LT]
    J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, I, Springer-Verlag, New York, 1977.zbMATHGoogle Scholar
  12. [MS]
    V. Milman and G. Schechtmann, Asymptotic theory of finite dimensional normed spaces, In “Lecture Notes in Mathematics” 1200, Springer-Verlag, New York, 1986.Google Scholar
  13. [O]
    E. Odell, Applications of Ramsey theory to Banach space theory, In “Notes in Banach Spaces” (H.E. Lacey, ed.), Univ. of Texas Press, 1980, 379–404.Google Scholar
  14. [R]
    H. Rosenthal, On a theorem of Krivine concerning block finite representability of p in general Banach spaces, J. Fune. Anal. 28 (1978), 197–225.zbMATHCrossRefGoogle Scholar
  15. [S1]
    Th. Schlumprecht, An arbitrarily distortable Banach space, Israel J. Math. 76 (1991), 81–95.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [S2]
    Th. Schlumprecht, A complementably minimal Banach space not containing c o or p, In “Seminar Notes in Functional Analysis and PDE’s”, Louisiana State University (1991–1992), 169–181.Google Scholar
  17. [T]
    B.S. Tsirelson, Not every Banach space contains p or c o, Funct. Anal. Appi. 8 (1974), 138–141.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • E. Odell
    • 1
  • Th. Schlumprecht
    • 2
  1. 1.Department of MathematicsThe University of Texas at AustinAustinUSA
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

Personalised recommendations