{"paper":{"title":"Random Banach spaces. The limitations of the method","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"P. Mankiewicz, Stanislaw J. Szarek","submitted_at":"1993-05-11T20:56:21Z","abstract_excerpt":"We study the properties of \"generic\", in the sense of the Haar measure on the corresponding Grassmann manifold, subspaces of l^N_infinity of given dimension. We prove that every \"well bounded\" operator on such a subspace, say E, is a \"small\" perturbation of a multiple of identity, where \"smallness\" is defined intrinsically in terms of the geometry of E. In the opposite direction, we prove that such \"generic subspaces of l^N_infinity\" do admit \"nontrivial well bounded\" projections, which shows the \"near optimality\" of the first mentioned result, and proves the so called \"Pisier's dichotomy conj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9305203","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"}