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Suppose that $\\mathcal{N}$ is a nontrivial complete nest on a Hilbert space $H$. We show in this paper that $G\\in {alg\\mathcal{N}}$ is an all-derivable point if and only if $G\\neq0$."},"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":"1107.1931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-11T03:49:17Z","cross_cats_sorted":[],"title_canon_sha256":"715ade33ee4b7f3e3a24ac8fe208413b5b35b2a9c5102fc93fc7c4bf4fa90270","abstract_canon_sha256":"e640815280128474994a54f25bc6c1abd0281c646e27f73327a6d9d80b5949f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:33.850581Z","signature_b64":"2EU3tozaWPWbuuQGA/2lnUUicHfLRxKB6LzZlrQrWXbQxoCrnmaTSz4gUBEd1OQ07/T/WXPh4cL1omTTZ9aXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4dc259175e9a572f48eb5a856a99a4c40c0882b31436def348703c833d56886","last_reissued_at":"2026-05-18T04:18:33.850064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:33.850064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of all-derivable points in nest algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jun Zhu, Sha Zhao","submitted_at":"2011-07-11T03:49:17Z","abstract_excerpt":"Let $\\mathcal{A}$ be an operator algebra on a Hilbert space. We say that an element $G\\in {\\mathcal{A}}$ is an all-derivable point of ${\\mathcal{A}}$ if every derivable linear mapping $\\phi$ at $G$ (i.e. $\\phi(ST)=\\phi(S)T+S\\phi(T)$ for any $S,T\\in alg{\\mathcal{N}}$ with $ST=G$) is a derivation. Suppose that $\\mathcal{N}$ is a nontrivial complete nest on a Hilbert space $H$. We show in this paper that $G\\in {alg\\mathcal{N}}$ is an all-derivable point if and only if $G\\neq0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1931","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":"1107.1931","created_at":"2026-05-18T04:18:33.850142+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.1931v1","created_at":"2026-05-18T04:18:33.850142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1931","created_at":"2026-05-18T04:18:33.850142+00:00"},{"alias_kind":"pith_short_12","alias_value":"UTOCLELV5GSX","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UTOCLELV5GSXF5EO","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UTOCLELV","created_at":"2026-05-18T12:26:42.757692+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/UTOCLELV5GSXF5EOWWUFNKM2JR","json":"https://pith.science/pith/UTOCLELV5GSXF5EOWWUFNKM2JR.json","graph_json":"https://pith.science/api/pith-number/UTOCLELV5GSXF5EOWWUFNKM2JR/graph.json","events_json":"https://pith.science/api/pith-number/UTOCLELV5GSXF5EOWWUFNKM2JR/events.json","paper":"https://pith.science/paper/UTOCLELV"},"agent_actions":{"view_html":"https://pith.science/pith/UTOCLELV5GSXF5EOWWUFNKM2JR","download_json":"https://pith.science/pith/UTOCLELV5GSXF5EOWWUFNKM2JR.json","view_paper":"https://pith.science/paper/UTOCLELV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.1931&json=true","fetch_graph":"https://pith.science/api/pith-number/UTOCLELV5GSXF5EOWWUFNKM2JR/graph.json","fetch_events":"https://pith.science/api/pith-number/UTOCLELV5GSXF5EOWWUFNKM2JR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UTOCLELV5GSXF5EOWWUFNKM2JR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UTOCLELV5GSXF5EOWWUFNKM2JR/action/storage_attestation","attest_author":"https://pith.science/pith/UTOCLELV5GSXF5EOWWUFNKM2JR/action/author_attestation","sign_citation":"https://pith.science/pith/UTOCLELV5GSXF5EOWWUFNKM2JR/action/citation_signature","submit_replication":"https://pith.science/pith/UTOCLELV5GSXF5EOWWUFNKM2JR/action/replication_record"}},"created_at":"2026-05-18T04:18:33.850142+00:00","updated_at":"2026-05-18T04:18:33.850142+00:00"}