{"paper":{"title":"Banach Spaces from Barriers in High Dimensional Ellentuck Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.LO","authors_text":"Alvaro Arias, Gabriel Giron-Garnica, Jose G. Mijares, Natasha Dobrinen","submitted_at":"2018-01-08T00:11:11Z","abstract_excerpt":"A new hierarchy of Banach spaces $T_k(d,\\theta)$, $k$ any positive integer, is constructed using barriers in high dimensional Ellentuck spaces \\cite{DobrinenJSL15} following the classical framework under which a Tsirelson type norm is defined from a barrier in the Ellentuck space \\cite{Argyros/TodorcevicBK}. The following structural properties of these spaces are proved. Each of these spaces contains arbitrarily large copies of $\\ell_\\infty^n$, with the bound constant for all $n$. For each fixed pair $d$ and $\\theta$, the spaces $T_k(d,\\theta)$, $k\\ge 1$, are $\\ell_p$-saturated, forming natura"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02278","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"}