Non-linear operators and differentiability of Lipschitz functions

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...

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Bibliographic Details
Published in:arXiv.org 2021-09
Main Authors: Bachir, Mohammed, Tapia-García, Sebastián
Format: Article
Language:English
Subjects:
Banach spaces
Linear operators
Operators (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422