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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1006.1021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-06-05T05:33:25Z","cross_cats_sorted":[],"title_canon_sha256":"babaaee7d0ac9de9864397c1b90af9615dd4d3d5a91dfd048eb07934c47d005d","abstract_canon_sha256":"d85d2f7de6fa71913398dea678b19b7c408805f389c4c0225c98fb05bd6ed4c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:38.565345Z","signature_b64":"AHaMJODvQ6xG6mZ/6fNpmBrTaMCLzWIWNeZtZajQ8d72wtDEzK8f2JIPLVIGUVDyEzWaGqxEoNW5EwUJ/hWjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"538173fac256ebd28d92a92a29edd0a1ad12d98565ee7ceb212c1321297e5816","last_reissued_at":"2026-05-18T03:59:38.564656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:38.564656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $n \\geq 3$. 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