Geodesic
Strong subdifferentiability of norms and geometry of Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 493-502.

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The strong subdifferentiability of norms (i.e\. one-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund.
Classification : 46B03, 46B20, 46B26
Keywords: strong subdifferentiability of norms; Asplund spaces; renormings; weak compact generating 
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     title = {Strong subdifferentiability of norms and geometry of {Banach} spaces},
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Godefroy, G.; Montesinos, V.; Zizler, V. Strong subdifferentiability of norms and geometry of Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 493-502. http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a10/