Israel Journal of Mathematics

, Volume 54, Issue 3, pp 327–334

Renormages de Quelques(K)


  • Michel Talagrand
    • Equipe d’Analyse - ERA 294Université Paris 6

DOI: 10.1007/BF02764961

Cite this article as:
Talagrand, M. Israel J. Math. (1986) 54: 327. doi:10.1007/BF02764961


LetD([0, 1]) be the space of left continuous real valued functions on [0, 1] which have a right limit at each point. We show thatD([0, 1]) has no equivalent norm which is Gâteau differentiable. Hence the class of spaces which can be renormed by a Gâteau differentiable norm fails the three spaces property. We show that there is no norm on([0, Ω]) such that its dual is strictly convex. However, there is an equivalent Fréchet differentiable norm on this space.

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© Hebrew University 1986