{"paper":{"title":"Finite dimensional subspaces of noncommutative $L_p$ spaces","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Hun Hee Lee","submitted_at":"2007-11-08T06:39:05Z","abstract_excerpt":"We prove the following noncommutative version of Lewis's classical result. Every n-dimensional subspace E of Lp(M) (1<p<\\infty) for a von Neumann algebra M satisfies d_{cb}(E, RC^n_{p'}) \\leq c_p n^{\\abs{1/2-1/p}} for some constant c_p depending only on $p$, where $1/p +1/p' =1$ and $RC^n_{p'} = [R_n\\cap C_n, R_n+C_n]_{1/p'}$. Moreover, there is a projection $P:Lp(M) --> Lp(M)$ onto E with $\\norm{P}_{cb} \\leq c_p n^{\\abs{1/2-1/p}}.$ We follow the classical change of density argument with appropriate noncommutative variations in addition to the opposite trick."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1208","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"}