Geodesic
A Note on Preserved Smoothness
Serdica Mathematical Journal, Tome 22 (1996) no. 1, pp. 29-32.

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Let X be a Banach space equipped with norm || · ||. We say that || · || is Gâteaux differentiable at x if for every h ∈ SX(|| · ||), (∗) lim t→0 (||x + th|| − ||x||) / t exists. We say that the norm || · || is Gâteaux differentiable if || · || is Gâteaux differentiable at all x ∈ SX(|| · ||).
Keywords: Renormings, Gâteaux Differentiability, Octahedral Norms 
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Tang, Wee-Kee. A Note on Preserved Smoothness. Serdica Mathematical Journal, Tome 22 (1996) no. 1, pp. 29-32. http://geodesic.mathdoc.fr/item/SMJ2_1996_22_1_a2/