On Gateaux differentiable bump functions
Volume 118 / 1996
Studia Mathematica 118 (1996), 135-143
DOI: 10.4064/sm-118-2-135-143
Abstract
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.
