{"paper":{"title":"Homomorphisms into a simple Z-stable C*-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Huaxin Lin, Zhuang Niu","submitted_at":"2010-03-09T00:12:28Z","abstract_excerpt":"Let $A$ and $B$ be unital separable simple amenable \\CA s which satisfy the Universal Coefficient Theorem. Suppose {that} $A$ and $B$ are $\\mathcal Z$-stable and are of rationally tracial rank no more than one. We prove the following: Suppose that $\\phi, \\psi: A\\to B$ are unital {monomorphisms}. There exists a sequence of unitaries $\\{u_n\\}\\subset B$ such that $$ \\lim_{n\\to\\infty} u_n^*\\phi(a) u_n=\\psi(a)\\tforal a\\in A, $$ if and only if $$ [\\phi]=[\\psi]\\,\\,\\,\\text{in}\\,\\,\\, KL(A,B), \\phi_{\\sharp}=\\psi_{\\sharp}\\andeqn\\phi^{\\ddag}=\\psi^{\\ddag}, $$ where $\\phi_{\\sharp}, \\psi_{\\sharp}: \\aff(T(A))"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1760","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"}