{"paper":{"title":"Gruss inequality for some types of positive linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.OA"],"primary_cat":"math.FA","authors_text":"Jagjit Singh Matharu, Mohammad Sal Moslehian","submitted_at":"2014-11-01T16:29:30Z","abstract_excerpt":"Assuming a unitarily invariant norm $|||\\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\\cdot|||$ on matrix algebras $\\mathcal{M}_n$ for all finite values of $n$ via $|||A|||=|||A\\oplus 0|||$. We show that if $\\mathscr{A}$ is a $C^*$-algebra of finite dimension $k$ and $\\Phi: \\mathscr{A} \\to \\mathcal{M}_n$ is a unital completely positive map, then \\begin{equation*} |||\\Phi(AB)-\\Phi(A)\\Phi(B)||| \\leq \\frac{1}{4} |||I_{n}|||\\,|||I_{kn}||| d_A d_B \\end{equation*} for any $A,B \\in \\mathscr{A}$, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0134","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"}