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We show that $\\phi$ and $\\psi$ are approximately unitarily equivalent if and only if \\beq[\\phi]&=&[\\psi] {\\rm in} KL(C,A), \\phi_{\\sharp}&=&\\psi_{\\sharp}\\tand \\phi^{\\dag}&=&\\psi^{\\dag}, \\eneq where $\\phi_{\\sharp}$ and $\\psi_{\\sharp}$ are continuous affine maps from tracial state space $T(A)$ of $A$ to faithful tracial state space $T_{\\rm f}(C)$ of $C$ induced by $\\phi$ and $\\psi,$ respectively, and $\\phi^{\\ddag}$ and $","authors_text":"Huaxin Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-22T21:40:21Z","title":"Homomorphisms from AH-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4631","kind":"arxiv","version":6},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cd2ea27cfabbc3e192519b549f8496675eff39420cf05ffa640fbb46343f5403","target":"record","created_at":"2026-05-18T01:35:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c0ed207345011fa26d74188d269b8324ff718ab60e423271294913251e4e54ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-22T21:40:21Z","title_canon_sha256":"42b38784dead4eb37e277f56645a9739afca5bf18087dc8bdc60c96d8f6aab45"},"schema_version":"1.0","source":{"id":"1102.4631","kind":"arxiv","version":6}},"canonical_sha256":"410363dc46dfb76b0264dafa5ef50f9f3aa3f0c11d87e302a794d6c7a617a679","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"410363dc46dfb76b0264dafa5ef50f9f3aa3f0c11d87e302a794d6c7a617a679","first_computed_at":"2026-05-18T01:35:52.624612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:52.624612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z0yze2GvBDKQKE2vigM/aMVjQLnSy2xCsgBphDmmKh9xuTmRLFR5cT14cgEh27LnYCgtlfcD3U1SE3FYYGnRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:52.625452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4631","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd2ea27cfabbc3e192519b549f8496675eff39420cf05ffa640fbb46343f5403","sha256:f312c7344f5532b231bbf6040954e4a649bbc71ab5014193f809a39437b57298"],"state_sha256":"6ede0dc3aef1e82aaa7b745be5ea561cf2657fc5bd2a332997da49e443c89560"}