{"paper":{"title":"A Gruss inequality for n-positive linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Mohammad Sal Moslehian, Rajna Rajic","submitted_at":"2010-06-05T05:33:25Z","abstract_excerpt":"Let $\\mathscr{A}$ be a unital $C^*$-algebra and let $\\Phi: \\mathscr{A} \\to {\\mathbb B}({\\mathscr H})$ be a unital $n$-positive linear map between $C^*$-algebras for some $n \\geq 3$. We show that $$\\|\\Phi(AB)-\\Phi(A)\\Phi(B)\\| \\leq \\Delta(A,||\\cdot||)\\,\\Delta(B,||\\cdot||)$$ for all operators $A, B \\in \\mathscr{A}$, where $\\Delta(C,\\|\\cdot\\|)$ denotes the operator norm distance of $C$ from the scalar operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1021","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"}