Exploring Convexity in Normed Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913359485468672 |
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| author | Babb, Ryan Luis Acosta |
| author_facet | Babb, Ryan Luis Acosta |
| contents | Normed spaces appear to have very little going for them: aside from the hackneyed linear structure, you get a norm whose only virtue, aside from separating points, is the Triangle Inequality. What could you possibly prove with that? As it turns out, quite a lot. In this article we will start by considering basic convexity properties of normed spaces, and gradually build up to some of the highlights of Functional Analysis, emphasizing how these notions of convexity play a key role in proving many surprising and deep results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring Convexity in Normed Spaces Babb, Ryan Luis Acosta Functional Analysis 52A07, 46B10 Normed spaces appear to have very little going for them: aside from the hackneyed linear structure, you get a norm whose only virtue, aside from separating points, is the Triangle Inequality. What could you possibly prove with that? As it turns out, quite a lot. In this article we will start by considering basic convexity properties of normed spaces, and gradually build up to some of the highlights of Functional Analysis, emphasizing how these notions of convexity play a key role in proving many surprising and deep results. |
| title | Exploring Convexity in Normed Spaces |
| topic | Functional Analysis 52A07, 46B10 |
| url | https://arxiv.org/abs/2405.13463 |