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We characterize surjective isometries of $X(H).$ We prove that if $T$ is such an isometry then there exist Borel maps $a:\\Om\\to\\bbK$ and $\\sigma:\\Om\\lra\\Om$ and a strongly measurable operator map $S$ of $\\Om$ into $\\calB(H)$ so that for almost all $\\om$ $S(\\om)$ is a surjective isometry of $H$\n  and for any $f\\in X(H)$ $$Tf(\\om)=a(\\om)S(\\om)(f(\\sigma(\\om))) \\text{ a.e.}$$\n  As a c"},"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":"math/9411210","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1994-11-16T22:08:45Z","cross_cats_sorted":[],"title_canon_sha256":"bb36cd974b0e830c504fa01b4c6018dd568ef30d10d4e8b975fd9e8092e42c76","abstract_canon_sha256":"b5643b3f0f4c6f0140a1e9e80f015cd8fff5c6c0aa08cae3a7421b40a77ef685"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:50.895790Z","signature_b64":"OYxdnYi9weAJVdG9N/WhqrM9jLcKNQkXMztx1S6uDB1z1I2gZDHmCzA7MKiv7dPsWteS2qA23JfFcLSaIzgCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13b2c9c079ea7b37dffa16bb57159abf5dbe6cca4b7fb16b1b383364cb12b0d3","last_reissued_at":"2026-05-18T01:05:50.895187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:50.895187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isometries of Hilbert space valued function spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Beata Randrianantoanina","submitted_at":"1994-11-16T22:08:45Z","abstract_excerpt":"Let $X$ be a (real or complex) rearrangement-in\\-va\\-riant function space on $\\Om$ (where $\\Om = [0,1]$ or $\\Om \\subseteq \\bbN$) whose norm is not proportional to the $L_2$-norm. 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We characterize surjective isometries of $X(H).$ We prove that if $T$ is such an isometry then there exist Borel maps $a:\\Om\\to\\bbK$ and $\\sigma:\\Om\\lra\\Om$ and a strongly measurable operator map $S$ of $\\Om$ into $\\calB(H)$ so that for almost all $\\om$ $S(\\om)$ is a surjective isometry of $H$\n  and for any $f\\in X(H)$ $$Tf(\\om)=a(\\om)S(\\om)(f(\\sigma(\\om))) \\text{ a.e.}$$\n  As a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9411210","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":"math/9411210","created_at":"2026-05-18T01:05:50.895268+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9411210v1","created_at":"2026-05-18T01:05:50.895268+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9411210","created_at":"2026-05-18T01:05:50.895268+00:00"},{"alias_kind":"pith_short_12","alias_value":"COZMTQDZ5J5T","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"COZMTQDZ5J5TPX72","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"COZMTQDZ","created_at":"2026-05-18T12:25:47.102015+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/COZMTQDZ5J5TPX72C25VOFM2X5","json":"https://pith.science/pith/COZMTQDZ5J5TPX72C25VOFM2X5.json","graph_json":"https://pith.science/api/pith-number/COZMTQDZ5J5TPX72C25VOFM2X5/graph.json","events_json":"https://pith.science/api/pith-number/COZMTQDZ5J5TPX72C25VOFM2X5/events.json","paper":"https://pith.science/paper/COZMTQDZ"},"agent_actions":{"view_html":"https://pith.science/pith/COZMTQDZ5J5TPX72C25VOFM2X5","download_json":"https://pith.science/pith/COZMTQDZ5J5TPX72C25VOFM2X5.json","view_paper":"https://pith.science/paper/COZMTQDZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9411210&json=true","fetch_graph":"https://pith.science/api/pith-number/COZMTQDZ5J5TPX72C25VOFM2X5/graph.json","fetch_events":"https://pith.science/api/pith-number/COZMTQDZ5J5TPX72C25VOFM2X5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/COZMTQDZ5J5TPX72C25VOFM2X5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/COZMTQDZ5J5TPX72C25VOFM2X5/action/storage_attestation","attest_author":"https://pith.science/pith/COZMTQDZ5J5TPX72C25VOFM2X5/action/author_attestation","sign_citation":"https://pith.science/pith/COZMTQDZ5J5TPX72C25VOFM2X5/action/citation_signature","submit_replication":"https://pith.science/pith/COZMTQDZ5J5TPX72C25VOFM2X5/action/replication_record"}},"created_at":"2026-05-18T01:05:50.895268+00:00","updated_at":"2026-05-18T01:05:50.895268+00:00"}