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arXiv · 2110.13722

Porosity phenomena of non-expansive, Banach space mappings

Michael Dymond
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Abstract

For any non-trivial convex and bounded subset $C$ of a Banach space, we show that outside of a $\sigma$-porous subset of the space of non-expansive mappings $C\to C$, all mappings have the maximal Lipschitz constant one witnessed locally at typical points of $C$. This extends a result of Bargetz and the author from separable Banach spaces to all Banach spaces and the proof given is completely independent. We further establish a fine relationship between the classes of exceptional sets involved in this statement, captured by the hierarchy of notions of $\phi$-porosity.

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Michael Dymond. 2021-10-26. Porosity phenomena of non-expansive, Banach space mappings. https://arxiv.org/abs/2110.13722

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