Advertisement

Some useful facts about Banach spaces

  • J. Lindenstrauss
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1317)

Keywords

Banach Space Extreme Point Banach Lattice Separable Banach Space Convex Norm 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B]
    Y. Benyamini, The uniform classification of Banach spaces, Longhorn notes, University of Texas 1984–85.Google Scholar
  2. [Be]
    B. Beauzamy, Introduction to Banach spaces and their goemetry, North Holland Mathematical Studies 68, sectond edition, 1985.Google Scholar
  3. [Bo]
    R.D. Bourgin, Geometric aspects of convex sets with the Radon Nikodym Property, Springer Lecture Notes #993, 1983.Google Scholar
  4. [B.M]
    S. Banach and S. Mazur, Zur Theorie der linearen Dimension, Studia Math. 4(1933), 110–112.zbMATHGoogle Scholar
  5. [B.P]
    C. Bessaga and A. Pelczynski, Selected topics in infinite dimensional topology, Monografie Matematyczne 58, Warsaw 1975.Google Scholar
  6. [B.Ph]
    E. Bishop and R.R. Phelps, The support functionals of a convex set, Proc. Symp. Pure Math. AMS 7 (1963), 27–36.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [B.R]
    O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics I, Springer Verlag 1979.Google Scholar
  8. [B.S]
    Y. Benyamini and Y. Sternfeld, Spheres in infinite dimensional normed spaces are Lipschitz contractible, Proc. AMS 88 (1983), 439–445.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [D]
    J. Diestel, Geometry of Banach spaces, selected topics, Springer Lecture Notes #485, 1975.Google Scholar
  10. [D.G.L]
    W. Davis, N. Ghoussoub and J. Lindenstrauss, A lattice renorming theorem and applications to vector valued processes, Trans. AMS 263 (1981), 531–540.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [D.U]
    J. Diestel and J.J. Uhl, Vector measures, Math. Surveys 15 AMS, 1977.Google Scholar
  12. [E]
    P. Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math. 13 (1973), 281–288.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [G.M]
    N. Ghoussoub and B. Maurey, H δ embeddings in Hilbert space and optimization on G δ sets, Memoirs of the AMS, #349, 1986.Google Scholar
  14. [J1]
    R.C. James, Weakly compact sets, Trans. AMS 113 (1964), 129–140.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [J2]
    R.C. James, Some self dual properties of normed linear spaces, Ann. Math. Studies 69 (1972), 159–175.MathSciNetGoogle Scholar
  16. [K1]
    V. Klee, Some topological properties of convex sets, Trans. AMS 78 (1955), 30–45.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [K2]
    V. Klee, Some new results on smoothness and rotundity in normed linear spaces, Math. Ann 139 (1959), 51–63.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [L.O.S]
    J. Lindenstrauss, G. Olsen and Y. Sternfeld, The Poulsen simplex, Ann. Inst. Fourier 28 (1978), 91–114.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [L.S]
    P.K. Lin and Y. Sternfeld, Convex sets with the Lipschitz fixed point property are compact, Proc. AMS 93 (1985), 633–639.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [L.T1]
    J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Vol 1, Sequence spaces, Springer Verlag 1977.Google Scholar
  21. [L.T2]
    J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Vol 2, Function spaces, Springer Verlag 1979.Google Scholar
  22. [O.P]
    R.I. Ovsepian and A. Pelczynski, The existence in every separable Banach space of a fundamental total and bounded biorthogonal system. Studia Math. 54 (1975), 149–159.MathSciNetzbMATHGoogle Scholar
  23. [P]
    A. Pelczynski, Any separable Banach space admits for every ε > 0 fundamental and total biorthogonal sequences bounded by 1 + ε. Studia Math. 55 (1976), 295–304.MathSciNetzbMATHGoogle Scholar
  24. [Ph]
    R.R. Phelps, Lectures on Choquet's theorem, Van Nostrand Math. Studies 1966.Google Scholar
  25. [Pi]
    G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), 326–350.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [Po]
    E.T. Poulsen, A simplex with dense extreme boundary, Ann. Inst. Fourier 11 (1961), 83–87.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [Pr]
    D. Preiss, Differentiability of Lipshcitz functions on Banach spaces (to appear).Google Scholar
  28. [V]
    M.M Vainberg, Some questions of differential calculus in linear spaces, Uspehi Mat. Nauk 7 (50) (1952), 55–102.MathSciNetzbMATHGoogle Scholar
  29. [Z]
    M. Zippin, Banach spaces with separable duals, (to appear in Trans. AMS).Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. Lindenstrauss
    • 1
  1. 1.Hebrew UniversityJerusalemIsrael

Personalised recommendations