{"paper":{"title":"Test-space characterizations of some classes of Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.FA","authors_text":"Mikhail I. Ostrovskii","submitted_at":"2011-12-14T00:50:35Z","abstract_excerpt":"Let $\\mathcal{P}$ be a class of Banach spaces and let $T=\\{T_\\alpha\\}_{\\alpha\\in A}$ be a set of metric spaces. We say that $T$ is a set of {\\it test-spaces} for $\\mathcal{P}$ if the following two conditions are equivalent: (1) $X\\notin\\mathcal{P}$; (2) The spaces $\\{T_\\alpha\\}_{\\alpha\\in A}$ admit uniformly bilipschitz embeddings into $X$.\n  The first part of the paper is devoted to a simplification of the proof of the following test-space characterization obtained in M.I. Ostrovskii [Different forms of metric characterizations of classes of Banach spaces, Houston J. Math., to appear]:\n  For "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3086","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"}