On the differentiability of norms in Banach spaces

Document Type : Research Paper


Faculty of Basic Sciences, Santiago de Cali University, Valle del Cauca, Cali, Colombia


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.


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Volume 13, Issue 2
July 2022
Pages 2015-2023
  • Receive Date: 14 October 2020
  • Revise Date: 16 December 2020
  • Accept Date: 26 December 2020