{"paper":{"title":"Modified mixed Tsirelson spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Manoussakis, Denka Kutzarova, Irene Deliyanni, Spiros A. Argyros","submitted_at":"1997-04-21T00:00:00Z","abstract_excerpt":"We study the modified and boundedly modified mixed Tsirelson spaces $T_M[({\\cal F}_{k_n},\\theta_n)_{n=1}^{\\infty }]$ and $T_{M(s)}[({\\cal F}_{k_n},\\theta_n)_{n=1}^{\\infty }]$ respectively, defined by a subsequence $({\\cal F}_{k_n})$ of the sequence of Schreier families $({\\cal F}_n)$. These are reflexive asymptotic $\\ell_1$ spaces with an unconditio- nal basis $(e_i)_i$ having the property that every sequence $\\{ x_i\\}_{i=1}^n$ of normalized disjointly supported vectors contained in $\\langle e_i\\rangle_{i=n}^{\\infty }$ is equivalent to the basis of $\\ell_1^n$. We show that if $\\lim\\theta_n^{1/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9704215","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}