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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.04292 |
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| _version_ | 1866917913042092032 |
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| author | Bargetz, Christian Dymond, Michael Pirk, Katriin |
| author_facet | Bargetz, Christian Dymond, Michael Pirk, Katriin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On extremal nonexpansive mappings Bargetz, Christian Dymond, Michael Pirk, Katriin Functional Analysis 46B25, 47H09, 54E52 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. |
| title | On extremal nonexpansive mappings |
| topic | Functional Analysis 46B25, 47H09, 54E52 |
| url | https://arxiv.org/abs/2409.04292 |