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arXiv · 2409.04292

On extremal nonexpansive mappings

Christian Bargetz·Michael Dymond·Katriin Pirk
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Abstract

We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometries are extremal in this sense for many Banach spaces, including Banach spaces with the Radon-Nikodym property and all $C(K)$-spaces for compact Hausdorff $K$. We also conclude that the typical, in the sense of Baire category, nonexpansive mapping is close to being extremal.

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Christian Bargetz, Michael Dymond, Katriin Pirk. 2024-09-06. On extremal nonexpansive mappings. https://arxiv.org/abs/2409.04292

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