Renormages de Quelquesℒ(K)
- 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 onℒ([0, Ω]) such that its dual is strictly convex. However, there is an equivalent Fréchet differentiable norm on this space.