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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/2409.04444 |
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| _version_ | 1866910593188888576 |
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| author | Maier, Beatrice Netzer, Tim |
| author_facet | Maier, Beatrice Netzer, Tim |
| contents | We show that the Carathéodory number of the joint numerical range of $d$ many bounded self-adjoint operators is at most $d-1$, and even at most $d-2$ if the underlying Hilbert space has dimension at least $3$. This extension of the classical convexity results for numerical ranges shows that also joint numerical ranges are significantly less non-convex than general sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04444 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on the Carathéodory Number of the Joint Numerical Range Maier, Beatrice Netzer, Tim Functional Analysis We show that the Carathéodory number of the joint numerical range of $d$ many bounded self-adjoint operators is at most $d-1$, and even at most $d-2$ if the underlying Hilbert space has dimension at least $3$. This extension of the classical convexity results for numerical ranges shows that also joint numerical ranges are significantly less non-convex than general sets. |
| title | A Note on the Carathéodory Number of the Joint Numerical Range |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2409.04444 |