Geodesic
On Gateaux differentiable bump functions
Studia Mathematica, Tome 118 (1996) no. 2, pp. 135-143

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI

It is shown that the order of Gateaux smoothness of bump functions on a wide class of Banach spaces with unconditional basis is not better than that of Fréchet differentiability. It is proved as well that in the separable case this order for Banach lattices satisfying a lower p-estimate for 1≤ p 2 can be only slightly better. 
Francisco L. Hernández. On Gateaux differentiable bump functions. Studia Mathematica, Tome 118 (1996) no. 2, pp. 135-143. doi: 10.4064/sm-118-2-135-143
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