{"paper":{"title":"$\\ell_p$ (p>2) does not coarsely embed into a Hilbert space","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"N. L. Randrianarivony, W. B. Johnson","submitted_at":"2004-10-19T19:20:48Z","abstract_excerpt":"A coarse embedding of a metric space X into a metric space Y is a map f: X-->Y satisfying for every x, y in X:\n  \\phi_1(d(x,y)) \\leq d(f(x),f(y)) \\leq \\phi_2(d(x,y))\n where \\phi_1 and \\phi_2 are nondecreasing functions on [0,\\infty) with values in [0,\\infty), with the condition that \\phi_1(t) tends to \\infty as t tends to \\infty. We show that \\ell_p does not coarsely embed in a Hilbert space for 2<p<\\infty."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410427","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"}