{"paper":{"title":"Higher Order Spreading Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"K. Tyros, S. A. Argyros, V. Kanellopoulos","submitted_at":"2012-02-28T21:52:17Z","abstract_excerpt":"We introduce the higher order spreading models associated to a Banach space $X$. Their definition is based on $\\ff$-sequences $(x_s)_{s\\in\\ff}$ with $\\ff$ a regular thin family and the plegma families. We show that the higher order spreading models of a Banach space $X$ form an increasing transfinite hierarchy $(\\mathcal{SM}_\\xi(X))_{\\xi<\\omega_1}$. Each $\\mathcal{SM}_\\xi (X)$ contains all spreading models generated by $\\ff$-sequences $(x_s)_{s\\in\\ff}$ with order of $\\ff$ equal to $\\xi$. We also provide a study of the fundamental properties of the hierarchy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6390","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"}