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Then for each $a\\in A$ there exists a tripotent $u_a$ in the bidual, $B'',$ of $B$ such that \\begin{enumerate}[$(a)$] \\item $\\{u_a,T(\\{f,g,h\\}),u_a\\}=\\{u_a,\\{T(f),T(g),T(h)\\},u_a\\}$, for all $f,g,h$ in the real JB$^*$-subtriple, $A_a,$ generated by $a$; \\item The mapping $\\{u_a,T(\\cdot),u_a\\} :A_a\\rightarrow B''$ is a linear isometry. \\end{enumerate} Furthermore, when $B$ is a real C$^*$-algebra, the projection $p=p_a= u_a^* u_a$ satisfies that $T(\\cdot)p :A_a\\rightarrow B''$ is an isometric trip"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.3838","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.OA","submitted_at":"2013-09-16T07:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"cf9b80fc1efa279df93ca255219b7f27461bb1d88065afdfc4d81d759b1fc854","abstract_canon_sha256":"21185c64e3396f15b623079fca0464fbc8bb5d97dee84e200d4ba846c60beac8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:12.272654Z","signature_b64":"GLER1Dx6flXxwRSk6J/7FZ2y5PdBJfG8GhXz7ALxCnQ4GunJIZ5/+UpiQ7UnCasymh5B+og8R0TMVdnJ5M8uAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f8602ea8e3b85a2041f509c19a562edec5a44e28fa96cf13831b499411e361d","last_reissued_at":"2026-05-18T03:13:12.271924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:12.271924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear isometries between real JB*-triples and C*-algebras","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Maria Apazoglou","submitted_at":"2013-09-16T07:27:52Z","abstract_excerpt":"Let $T: A\\to B$ be a (not necessarily surjective) linear isometry between two real JB$^*$-triples. Then for each $a\\in A$ there exists a tripotent $u_a$ in the bidual, $B'',$ of $B$ such that \\begin{enumerate}[$(a)$] \\item $\\{u_a,T(\\{f,g,h\\}),u_a\\}=\\{u_a,\\{T(f),T(g),T(h)\\},u_a\\}$, for all $f,g,h$ in the real JB$^*$-subtriple, $A_a,$ generated by $a$; \\item The mapping $\\{u_a,T(\\cdot),u_a\\} :A_a\\rightarrow B''$ is a linear isometry. \\end{enumerate} Furthermore, when $B$ is a real C$^*$-algebra, the projection $p=p_a= u_a^* u_a$ satisfies that $T(\\cdot)p :A_a\\rightarrow B''$ is an isometric trip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3838","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.3838","created_at":"2026-05-18T03:13:12.272020+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.3838v1","created_at":"2026-05-18T03:13:12.272020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3838","created_at":"2026-05-18T03:13:12.272020+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6DAF2UOHOC2","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6DAF2UOHOC2EBA7","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6DAF2UO","created_at":"2026-05-18T12:27:57.521954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X","json":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X.json","graph_json":"https://pith.science/api/pith-number/R6DAF2UOHOC2EBA7KCOBTJLC5X/graph.json","events_json":"https://pith.science/api/pith-number/R6DAF2UOHOC2EBA7KCOBTJLC5X/events.json","paper":"https://pith.science/paper/R6DAF2UO"},"agent_actions":{"view_html":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X","download_json":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X.json","view_paper":"https://pith.science/paper/R6DAF2UO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.3838&json=true","fetch_graph":"https://pith.science/api/pith-number/R6DAF2UOHOC2EBA7KCOBTJLC5X/graph.json","fetch_events":"https://pith.science/api/pith-number/R6DAF2UOHOC2EBA7KCOBTJLC5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X/action/storage_attestation","attest_author":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X/action/author_attestation","sign_citation":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X/action/citation_signature","submit_replication":"https://pith.science/pith/R6DAF2UOHOC2EBA7KCOBTJLC5X/action/replication_record"}},"created_at":"2026-05-18T03:13:12.272020+00:00","updated_at":"2026-05-18T03:13:12.272020+00:00"}