Geodesic
Smoothability, Strong Smoothability and Dentability in Banach Spaces1
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 59-68

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

It is shown that dentability of the unit ball of a conjugate Banach space X* does not imply smoothability of the unit ball of X, answering a question raised by Kemp. A property called strong smoothability is introduced and is shown to be dual to dentability. The results are used to provide new proofs of the facts that X is an Asplund space whenever it has an equivalent Fréchet differentiable norm, or whenever X* has the Radon-Nikodym Property. 
Anantharaman, R.; Lewis, T.; Whitfield, J. H. M. Smoothability, Strong Smoothability and Dentability in Banach Spaces1. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 59-68. doi: 10.4153/CMB-1981-009-9
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