Geodesic
A Non-Reflexive Smooth Space with a Smooth Dual
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 579-580

Voir la notice de l'article provenant de la source Cambridge University Press

Let (E, ρ) and (E *ρ *) be a real Banach space and its dual. Restrepo has shown in [4] that, if p and ρ * are both Fréchet differentiable, E is reflexive. The purpose of this note is to show that Fréchet differentiability cannot be replaced by Gateaux differentiability. This answers negatively a question raised by Wulbert [5]. In particular, we will renorm a certain nonreflexive space with a smooth norm whose dual is also smooth. 
Whitfield, J. H. M. A Non-Reflexive Smooth Space with a Smooth Dual. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 579-580. doi: 10.4153/CMB-1974-103-4
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[5] 5. Wulbert, D., Approximation by Ck-functions, Proc. Sympos. on Approx. Theory Austin, 1973, Academic Press (to appear). Google Scholar

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