{"paper":{"title":"Bilocal *-automorphisms of B(H) satisfying the 3-local property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ahlem Ben Ali Essaleh, Antonio M. Peralta, Mohsen Niazi","submitted_at":"2014-12-05T08:40:22Z","abstract_excerpt":"We prove that, for a complex Hilbert space $H$ with dimension bigger or equal than three, every linear mapping $T: B(H)\\to B(H)$ satisfying the 3-local property is a $^*$-monomorphism, that is, every linear mapping $T: B(H) \\to B(H)$ satisfying that for every $a$ in $B(H)$ and every $\\xi,\\eta$ in $H$, there exists a $^*$-automorphism $\\pi_{a,\\xi,\\eta}: B(H)\\to B(H)$, depending on $a$, $\\xi$, and $\\eta$, such that $$T(a) (\\xi) = \\pi_{a,\\xi,\\eta} (a) (\\xi), \\hbox{ and } T(a) (\\eta) = \\pi_{a,\\xi,\\eta} (a) (\\eta),$$ is a $^*$-monomorphism. This solves a question posed by L. Moln\\'ar in [\\emph{Arch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1918","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"}