{"paper":{"title":"On a tensor-analogue of the Schur product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"K. Sumesh, V.S. Sunder","submitted_at":"2015-09-16T11:01:22Z","abstract_excerpt":"We consider the tensorial Schur product $R \\circ^\\otimes S = [r_{ij} \\otimes s_{ij}]$ for $R \\in M_n(\\mathcal{A}), S\\in M_n(\\mathcal{B}),$ with $\\mathcal{A}, \\mathcal{B}$ unital $C^*$-algebras, verify that such a `tensorial Schur product' of positive operators is again positive, and then use this fact to prove (an apparently marginally more general version of) the classical result of Choi that a linear map $\\phi:M_n \\to M_d$ is completely positive if and only if $[\\phi(E_{ij})] \\in M_n(M_d)^+$, where of course $\\{E_{ij}:1 \\leq i,j \\leq n\\}$ denotes the usual system of matrix units in $M_n (:= "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04884","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"}