Pacific Journal of Mathematics

Geometrical implications of upper semi-continuity of the duality mapping on a Banach space.

J. R. Giles, D. A. Gregory, and Brailey Sims

Article information

Pacific J. Math., Volume 79, Number 1 (1978), 99-109.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces


Giles, J. R.; Gregory, D. A.; Sims, Brailey. Geometrical implications of upper semi-continuity of the duality mapping on a Banach space. Pacific J. Math. 79 (1978), no. 1, 99--109.

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  • [1] E. Asplund, R. T. Rockafellar, Gradients of convex functions, Trans. Amer. Math. Soc, 139 (1969), 443-467.
  • [2] B. Bollobas, An extension to the theorem of Bishop and Phelps, Bull. London Math. Soc, 2 (1970), 181-182.
  • [3] F. F. Bonsall, B. E. Cain and H. Schneider, The numericalrange of a continuous mapping of a normed space, Aeq. Math., 2 (1968), 86-93.
  • [4] D. F. Cudia, The geometry of Banach spaces. Smoothness, Trans. Amer. Math. Soc, 110 (1964), 284-314.
  • [5] J. Diestel and B. Faires, On vector measures, Trans. Amer. Math. Soc, 198 (1974), 253-271.
  • [6] I. Ekeland and G. Lebourg, Generic Frechet differentiabilityand perturbed optimi- aztion problems in Banach spaces, Trans. Amer. Math. Soc, 224 (1976), 193-216.
  • [7] J. R. Giles, On a characterizationof differentiabilityof the norm of a normed linear space, J. Austral. Math. Soc, 12 (1971), 106-114.
  • [8] J. R. Giles, On smoothness of the Banach space embedding, Bull. Austral. Math. Soc, 13 (1975), 69-74.
  • [9] J. L. Kelley and I. Namioka, LinearTopological Spaces, van Nostrand, 1963.
  • [10] P. Kenderov, Semi-continuityof set-valued monotone mappings, Fund. Math., 88 (1975), 61-69.
  • [11] P. Kenderov, Monotone operators in Asplund spaces, to appear in C. R. Acad. Bulgar. Sci.
  • [12] I. Namioka and R. R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J., 42 (1975), 735-750.
  • [13] M. A. Smith and F. Sullivan, Extremelysmooth Banach spaces, (preprint).
  • [14] V. L. Smulian, Sur la derivabilite de la norme dans Vespace de Banach, Dokl. Akad. Nauk. SSSR, 27 (1940), 643-648.
  • [15] C. Stegall, The duality between Asplund spaces and spaces with theRadon-Nikodym property, Israel J. Math., (to appear).