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Extremely smooth Banach spaces

  • Mark A. Smith
  • Francis Sullivan
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 604)

Keywords

Banach Space Finite Dimensional Subspace Conjugate Space Contractive Projection Smooth Space 
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.
    E. Bishop and R. R. Phelps, The support functionals of a convex set, Convexity, 27–35 (Proc. Sympos. Pure Math. 7 Amer. Math. Soc., Providence, Rhode Island, 1963).Google Scholar
  2. 2.
    A. L. Brown, On the canonical projection of the third dual of a Banach space onto the first dual, (to appear).Google Scholar
  3. 3.
    M. M. Day, Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc. 78(1955), 516–528.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    _____, Normed linear spaces, 3rd ed. (Ergebnisse der Mathematik und ihrer Grenzgebiete, 21. Springer-Verlag, Berlin, Heidelberg, New York, 1973).Google Scholar
  5. 5.
    D. W. Dean, The equation L(E,X**)=L(E,X)** and the principle of local reflexivity, Proc. Amer. Math. Soc. 40(1973), 146–148.MathSciNetzbMATHGoogle Scholar
  6. 6.
    J. Diestel and B. Faires, On vector measures, Trans. Amer. Math. Soc. 198(1974), 253–271.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    J. Dixmier, Sur un theoreme de Banach, Duke Math. J. 15(1948), 1057–1071.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    J. R. Giles, On smoothness of the Banach space embedding, Bull. Austral. Math. Soc. 13(1975), 69–74.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    J. Lindenstrauss and H. P. Rosenthal, The ℒp spaces, Israel J. Math. 7(1969), 325–349.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    I. Namioka and R. R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J. 42(1975), 735–750.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    J. Rainwater, A non-reflexive Banach space has non-smooth third conjugate space, unpublished note.Google Scholar
  12. 12.
    I. Singer, On the problem of non-smoothness of non-reflexive second conjugate spaces, Bull. Austral. Math. Soc. 12(1975), 407–416.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    M. A. Smith, A smooth, non-reflexive second conjugate space, Bull. Austral. Math. Soc. 15(1976), 129–131.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    _____, Rotundity and smoothness in conjugate spaces, (to appear).Google Scholar
  15. 15.
    F. Sullivan, Geometrical properties determined by the higher duals of a Banach space, (to appear).Google Scholar
  16. 16.
    D. G. Tacon, The conjugate of a smooth Banach space, Bull. Austral. Math. Soc. 2(1970), 415–425.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    S. Troyanski, Example of a smooth space whose conjugate has not strictly convex norm, Studia Math. 35(1970), 305–309.MathSciNetGoogle Scholar
  18. 18.
    J. J. Uhl, Jr., A note on the Radon-Nikodym property, Revue Roumaine de Math. Pures et Appl. 17(1972), 113–115.MathSciNetzbMATHGoogle Scholar
  19. 19.
    L. P. Vlasov, Approximative properties of sets in normed linear spaces, Russian Math. Surveys 28(1973), 1–66.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Mark A. Smith
    • 1
  • Francis Sullivan
    • 2
  1. 1.Department of MathematicsLake Forest CollegeLake ForestUSA
  2. 2.Department of MathematicsThe Catholic University of AmericaWashington, D.C.USA

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