{"paper":{"title":"Cones with a Mapping Cone Symmetry in the Finite-Dimensional Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.OA","authors_text":"{\\L}ukasz Skowronek","submitted_at":"2010-08-19T08:22:15Z","abstract_excerpt":"In the finite-dimensional case, we present a new approach to the theory of cones with a mapping cone symmetry, first introduced by St{\\o}rmer. Our method is based on a definition of an inner product in the space of linear maps between two algebras of operators and the fact that the Jamio{\\l}kowski-Choi isomorphism is an isometry. We consider a slightly modified class of cones, although not substantially different from the original mapping cones by St{\\o}rmer. Using the new approach, several known results are proved faster and often in more generality than before. For example, the dual of a map"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3237","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"}