Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911767387439104 |
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| author | Chu, Hung Viet Schlumprecht, Thomas |
| author_facet | Chu, Hung Viet Schlumprecht, Thomas |
| contents | We prove that for every countable ordinal $ξ$, the Tsirelson's space $T_ξ$ of order $ξ$, is naturally, i.e., via the identity, $3$-isomorphc to its modified version. For the first step, we prove that the Schreier family $\mathcal{S}_ξ$ is the same as its modified version $ \mathcal{S}^M_ξ$, thus answering a question by Argyros and Tolias. As an application, we show that the algebra of linear bounded operators on $T_ξ$ has $2^{\mathfrak c}$ closed ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16491 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic Chu, Hung Viet Schlumprecht, Thomas Functional Analysis 46B20 (primary), 46B06, 46B25 (secondary) We prove that for every countable ordinal $ξ$, the Tsirelson's space $T_ξ$ of order $ξ$, is naturally, i.e., via the identity, $3$-isomorphc to its modified version. For the first step, we prove that the Schreier family $\mathcal{S}_ξ$ is the same as its modified version $ \mathcal{S}^M_ξ$, thus answering a question by Argyros and Tolias. As an application, we show that the algebra of linear bounded operators on $T_ξ$ has $2^{\mathfrak c}$ closed ideals. |
| title | Higher Order Tsirelson Spaces and their Modified Versions are Isomorphic |
| topic | Functional Analysis 46B20 (primary), 46B06, 46B25 (secondary) |
| url | https://arxiv.org/abs/2401.16491 |