Twisted Hilbert spaces defined by bi-Lipschitz maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917749916172288 |
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| author | Corrêa, Willian Dantas, Sheldon Rodríguez-Vidanes, Daniel L. |
| author_facet | Corrêa, Willian Dantas, Sheldon Rodríguez-Vidanes, Daniel L. |
| contents | We obtain an infinite-dimensional cone of singular twisted Hilbert spaces $Z(φ)$ which are isomorphic to their duals but not to their conjugate duals. We do that by showing that the subset of all bi-Lipschitz maps from $[0, \infty)$ to $\mathbb{R}$ is coneable. We also provide a characterization of the Kalton-Peck space among all twisted Hilbert spaces of the form $Z(φ)$, which gives a partial answer to a conjecture of F. Cabello Sánchez and J. Castillo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted Hilbert spaces defined by bi-Lipschitz maps Corrêa, Willian Dantas, Sheldon Rodríguez-Vidanes, Daniel L. Functional Analysis We obtain an infinite-dimensional cone of singular twisted Hilbert spaces $Z(φ)$ which are isomorphic to their duals but not to their conjugate duals. We do that by showing that the subset of all bi-Lipschitz maps from $[0, \infty)$ to $\mathbb{R}$ is coneable. We also provide a characterization of the Kalton-Peck space among all twisted Hilbert spaces of the form $Z(φ)$, which gives a partial answer to a conjecture of F. Cabello Sánchez and J. Castillo. |
| title | Twisted Hilbert spaces defined by bi-Lipschitz maps |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2408.07827 |