%0 Journal Article
%T On the differentiability of norms in Banach spaces
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Munoz-Tello, Andres Felipe
%D 2022
%\ 07/01/2022
%V 13
%N 2
%P 2015-2023
%! On the differentiability of norms in Banach spaces
%K Gâteaux differentiable
%K Fréchet differentiable
%K locally Lipschitz function
%K Gauss null set
%R 10.22075/ijnaa.2020.22114.2329
%X The purpose of this paper is to show some particularities that the differentiability sets generated from the norms have in the Banach spaces. In this sense, it will be shown that the Gaussian measure of the Fr\'echet differentiability set of the norm of the space $\ell^{\infty}(\mathbb{R})$ of real bounded sequences is zero and that in the case of the space $BV[a,b]$ of bounded variation functions its norm is not Fr\'echet derivable in any element of this space.
%U https://ijnaa.semnan.ac.ir/article_6598_63be541a21b7be46d75a4f7b10d8c99f.pdf