{"paper":{"title":"Weak-2-local symmetric maps on C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Juan Carlos Cabello","submitted_at":"2015-10-04T08:28:18Z","abstract_excerpt":"We introduce and study weak-2-local symmetric maps between C$^*$-algebras $A$ and $B$ as non necessarily linear nor continuous maps $\\Delta: A\\to B$ such that for each $a,b\\in A$ and $\\phi\\in B^{*}$, there exists a symmetric linear map $T_{a,b,\\phi}: A\\to B$, depending on $a$, $b$ and $\\phi$, satisfying $\\phi \\Delta(a) = \\phi T_{a,b,\\phi}(a)$ and $\\phi \\Delta(b) = \\phi T_{a,b,\\phi}(b)$. We prove that every weak-2-local symmetric map between C$^*$-algebras is a linear map. Among the consequences we show that every weak-2-local $^*$-derivation on a general C$^*$-algebra is a (linear) $^*$-deriva"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00915","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"}