A remark on the distortion of twisted sums
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914730190307328 |
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| author | Suárez, Jesús |
| author_facet | Suárez, Jesús |
| contents | Odell and Schlumprecht solved the distortion problem by proving that the classic sequence spaces $\ell_p$ for $1<p<\infty$ admit an inevitable biorthogonal system. In particular, these spaces are arbitrarily distortable. Later, Maurey extended the result to asymptotic $\ell_p$-spaces while Tomczak-Jaegermann did likewise for the Schatten classes. We observe that the Kalton-Peck spaces $Z_p$ for $1<p<\infty$ admit an inevitable biorthogonal system. Therefore, we may add this classic family to the list of arbitrarily distortable spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A remark on the distortion of twisted sums Suárez, Jesús Functional Analysis 46B03, 46B20, 46B06 Odell and Schlumprecht solved the distortion problem by proving that the classic sequence spaces $\ell_p$ for $1<p<\infty$ admit an inevitable biorthogonal system. In particular, these spaces are arbitrarily distortable. Later, Maurey extended the result to asymptotic $\ell_p$-spaces while Tomczak-Jaegermann did likewise for the Schatten classes. We observe that the Kalton-Peck spaces $Z_p$ for $1<p<\infty$ admit an inevitable biorthogonal system. Therefore, we may add this classic family to the list of arbitrarily distortable spaces. |
| title | A remark on the distortion of twisted sums |
| topic | Functional Analysis 46B03, 46B20, 46B06 |
| url | https://arxiv.org/abs/2403.18037 |