{"paper":{"title":"Proximity to $\\ell_1$ and Distortion in Asymptotic $\\ell_1$ Spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Edward Odell, Nicole Tomczak-Jaegermann, Roy Wagner","submitted_at":"1997-04-09T00:00:00Z","abstract_excerpt":"For an asymptotic $\\ell_1$ space $X$ with a basis $(x_i)$ certain asymptotic $\\ell_1$ constants, $\\delta_\\alpha (X)$ are defined for $\\alpha <\\omega_1$. $\\delta_\\alpha (X)$ measures the equivalence between all normalized block bases $(y_i)_{i=1}^k$ of $(x_i)$ which are $S_\\alpha$-admissible with respect to $(x_i)$ ($S_\\alpha$ is the $\\alpha^{th}$-Schreier class of sets) and the unit vector basis of $\\ell_1^k$. This leads to the concept of the delta spectrum of $X$, $\\Delta (X)$, which reflects the behavior of stabilized limits of $\\delta_\\alpha (X)$. The analogues of these constants under all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9704214","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"}