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Exploring convexity in normed spaces
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Acosta Babb, Ryan L. (2024) Exploring convexity in normed spaces. American Mathematical Monthly . ISSN 0002-9890. (In Press)
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Abstract
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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | American Mathematical Monthly | ||||||
| Publisher: | Mathematical Association of America | ||||||
| ISSN: | 0002-9890 | ||||||
| Official Date: | 2024 | ||||||
| Dates: |
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| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| Re-use Statement: | This is an Accepted Manuscript of an article published by Taylor & Francis in American Mathematical Monthly on [date of publication], available at: https://doi.org/[Article DOI]. | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 23 May 2024 | ||||||
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