Archiv der Mathematik

, Volume 58, Issue 5, pp 471–476

Fréchet differentiable norms on spaces of countable dimension

  • Jon Vanderwerff


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  1. [1]
    W. J. Davis andW. B. Johnson, A renorming of nonreflexive Banach spaces. Proc. Amer. Math. Soc.37, 486–489 (1973).Google Scholar
  2. [2]
    J.Diestel, Geometry of Banach spaces — Selected topics. LNM485, Berlin-Heidelberg-New York 1975.Google Scholar
  3. [3]
    M. Fabian, L. Zajíček andV. Zizler, On residuality of the set of rotund norms on a Banach space. Math. Ann.258, 349–351 (1982).Google Scholar
  4. [4]
    K. John andV. Zizler, A short proof of a version of Asplund's norm averaging theorem. Proc. Amer. Math. Soc.73, 277–278 (1979).Google Scholar
  5. [5]
    W. B. Johnson, H. P. Rosenthal andM. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach spaces. Israel J. Math.9, 488–506 (1971).Google Scholar
  6. [6]
    M. I. Kadets, Spaces isomorphic to a locally uniformly convex space. (Russian) Izv. Vysš. Učebn. Zaved. Mat.13, 51–57 (1959).Google Scholar
  7. [7]
    M. I. Kadets, A proof of the topological equivalence of all separable infinite-dimensional Banach spaces. (Russian) Funkcional. Anal. i. Priložen.1, 61–70 (1967).Google Scholar
  8. [8]
    J.Lindenstrauss and L.Tzafriri, Classical Banach spaces. I. Sequence spaces. Berlin-Heidelberg-New York 1977.Google Scholar
  9. [9]
    V. L. Šmulyan, Sur la dérivabilité de la norme dans l'espace de Banach. C. R. Acad. Sci. URSS (Doklady) N. S.27, 643–648 (1940).Google Scholar

Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • Jon Vanderwerff
    • 1
  1. 1.Department of MathematicsUniversity of AlbertaEdmontonCanada

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