{"paper":{"title":"Positive Linear Maps on Second Symmetric Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"K. C. Sivakumar, Pavankumar Raickwade","submitted_at":"2026-05-18T09:16:15Z","abstract_excerpt":"Let $X^{(2)}$ denote the second symmetric product space of a partially ordered vector space $X$, endowed with the projective cone. A characterization of linear maps $T\\colon X^{(2)}\\to X^{(2)}$ which preserve the set of all positive decomposable vectors, is proved. As applications of this result, an alternative proof, as well as an infinite dimensional generalization, of a representation theorem for (i) automorphisms on the completely positive cone and (ii) linear preservers of CP-rank-1 matrices, are presented. It is also shown that if $T$ preserves the set of all decomposable vectors, then s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18103","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18103/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T23:41:59.180422Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.418759Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"37051eea4ab9eea56fa30c2659caed84290ed619fc1e91bfc5ed7783a67668f6"},"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"}