{"paper":{"title":"On the ternary domain of a completely positive map on a Hilbert C*-module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Maria Joi\\c{t}a, Mohammad B. Asadi, Reza Behmani","submitted_at":"2018-10-21T16:27:06Z","abstract_excerpt":"We associate to an operator valued completely positive linear map $\\varphi$ on a $C^{\\ast }$-algebra $A$ and a Hilbert $C^{\\ast }$-module $X$ over $A$ a subset $X_{\\varphi }$ of $X,$ called '\\textit{ternary domain}' of $\\varphi$ on $X,$ which is a Hilbert $C^{\\ast }$-module over the multiplicative domain of $\\varphi $ and every $\\varphi $-map (i.e., associated quaternary map with $\\varphi $) acts on it as a ternary map. We also provide several characterizations for this set. The ternary domain \\ of $\\varphi $ on $A\\ $ is a closed two-sided $\\ast $-ideal $T_{\\varphi }$ of the multiplicative dom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08987","kind":"arxiv","version":3},"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"}