{"paper":{"title":"Perturbations of completely positive maps and strong NF algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Caleb Eckhardt","submitted_at":"2009-06-18T20:49:30Z","abstract_excerpt":"Let $\\phi:M_n\\to B(H)$ be an injective, completely positive contraction with $\\V\\phi^{-1}:\\phi(M_n)\\to M_n\\V_{cb}\\leq1+\\delta(\\epsilon).$ We show that if either (i) $\\phi(M_n)$ is faithful modulo the compact operators or (ii) $\\phi(M_n)$ approximately contains a rank 1 projection, then there is a complete order embedding $\\psi:M_n\\to B(H)$ with $\\V\\phi-\\psi\\V_{cb}<\\epsilon.$ We also give examples showing that such a perturbation does not exist in general. As an application, we show that every $C^*$-algebra $A$ with $\\mathcal{OL}_\\infty(A)=1$ and a finite separating family of primitive ideals i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3510","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"}