Characterization of Hilbertizable spaces via convex functions
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918052109484032 |
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| author | Borchard, Nicolas Wachsmuth, Gerd |
| author_facet | Borchard, Nicolas Wachsmuth, Gerd |
| contents | We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then the underlying space is also isomorphic to a Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04686 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of Hilbertizable spaces via convex functions Borchard, Nicolas Wachsmuth, Gerd Functional Analysis Optimization and Control 46C15, 46N10 We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then the underlying space is also isomorphic to a Hilbert space. |
| title | Characterization of Hilbertizable spaces via convex functions |
| topic | Functional Analysis Optimization and Control 46C15, 46N10 |
| url | https://arxiv.org/abs/2506.04686 |