{"paper":{"title":"Spreading Models in Banach Space Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.FA","authors_text":"K. Tyros, S.A. Argyros, V. Kanellopoulos","submitted_at":"2010-06-04T17:59:14Z","abstract_excerpt":"We extend the classical Brunel-Sucheston definition of the spreading model by introducing the $\\mathcal{F}$-sequences $(x_s)_{s\\in\\mathcal{F}}$ in a Banach space and the plegma families in $\\mathcal{F}$ where $\\mathcal{F}$ is a regular thin family. The new concept yields a transfinite increasing hierarchy of classes of spreading sequences. We explore the corresponding theory and we present examples establishing this hierarchy and illustrating the limitation of the theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0957","kind":"arxiv","version":2},"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"}