Porosity phenomena of non-expansive, Banach space mappings
Michael Dymond · arXiv (Cornell University) · 2021
For any non-trivial convex and bounded subset $C$ of a Banach space, we show that outside of a $σ$-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 $ϕ$-porosity.