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arXiv · 2110.00099

Non-linear operators and differentiability of Lipschitz functions

Mohammed Bachir·Sebastián Tapia-García
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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.

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Mohammed Bachir, Sebastián Tapia-García. 2021-09-30. Non-linear operators and differentiability of Lipschitz functions. https://arxiv.org/abs/2110.00099

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