Non-linear operators and differentiability of Lipschitz functions
Functional Analysis
2021-10-04 v1
Abstract
In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological and non-linear framework. Restricted to the linear case, we can apply our results to compact, weakly-compact, limited and completely continuous linear operators. Moreover, our results yield a characterization of Gelfand-Phillips spaces and recover some known result of Schur spaces and reflexive spaces concerning the differentiability of real-valued Lipschitz functions.
Cite
@article{arxiv.2110.00099,
title = {Non-linear operators and differentiability of Lipschitz functions},
author = {Mohammed Bachir and Sebastián Tapia-García},
journal= {arXiv preprint arXiv:2110.00099},
year = {2021}
}