Embedding $\ell_2$ and $J$ into subspaces of $JT$ and $JT^*$
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| Format: | Preprint |
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2026
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| _version_ | 1866912973032783872 |
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| author | Argyros, Spiros A. Gonzalez, Manuel Motakis, Pavlos |
| author_facet | Argyros, Spiros A. Gonzalez, Manuel Motakis, Pavlos |
| contents | In the first part of the paper we show that every closed subspace of $JT$ or $JT^*$ contains $\ell_2$ complemented in $JT$ or $JT^*$ respectively, and $JT$ contains uncomplemented copies of $\ell_2$. As a result, the predual $\B$ of $JT$, as well as the spaces $JT$ and $JT^*$, are subprojective and superprojective. In the second part, we prove that every weakly Cauchy sequence that is not weakly convergent in $JT$ has a subsequence equivalent to the basis of $J$. Hence, every non-reflexive subspace of $JT$ contains an isomorphic copy of $J$, and every Schauder basic sequence in $JT$ has a subsequence which is equivalent either to the basis of $\ell_2$ or to the basis of $J$. Moreover these subspaces may be selected to be complemented in $JT$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_17886 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Embedding $\ell_2$ and $J$ into subspaces of $JT$ and $JT^*$ Argyros, Spiros A. Gonzalez, Manuel Motakis, Pavlos Functional Analysis Primary 46B03, 46B20 In the first part of the paper we show that every closed subspace of $JT$ or $JT^*$ contains $\ell_2$ complemented in $JT$ or $JT^*$ respectively, and $JT$ contains uncomplemented copies of $\ell_2$. As a result, the predual $\B$ of $JT$, as well as the spaces $JT$ and $JT^*$, are subprojective and superprojective. In the second part, we prove that every weakly Cauchy sequence that is not weakly convergent in $JT$ has a subsequence equivalent to the basis of $J$. Hence, every non-reflexive subspace of $JT$ contains an isomorphic copy of $J$, and every Schauder basic sequence in $JT$ has a subsequence which is equivalent either to the basis of $\ell_2$ or to the basis of $J$. Moreover these subspaces may be selected to be complemented in $JT$. |
| title | Embedding $\ell_2$ and $J$ into subspaces of $JT$ and $JT^*$ |
| topic | Functional Analysis Primary 46B03, 46B20 |
| url | https://arxiv.org/abs/2603.17886 |