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Let $\\mathcal{N}$ be a non-trivial nest on $\\mathcal{X}$, ${\\rm Alg}\\mathcal{N}$ be the nest algebra associated with $\\mathcal{N}$, and $L\\colon {\\rm Alg}\\mathcal{N}\\longrightarrow \\mathcal{B(X)}$ be a linear mapping. Suppose that $p_n(x_1,x_2,\\cdots,x_n)$ is an $(n-1)$-th commutator defined by $n$ indeterminates $x_1, x_2, \\cdots, x_n$. It is shown that $L$ satisfies the rule $$ L(p_n(A_1, A_2, \\cdots, A_n))=\\sum_{k=1}^{n}p_n(A_1, \\cdots"},"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":"1706.02951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-09T13:54:15Z","cross_cats_sorted":["math.OA","math.RA"],"title_canon_sha256":"6916543b687e015146167c3f16388540a016c9b4f4544f60840203049e468d53","abstract_canon_sha256":"973bc4b086e73c8646a14d02eaecf81f5d3c212b5ba3b059a0e10c9ea4db3a17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:40.479556Z","signature_b64":"90o6ZlQ7ZnRVqQcwVSr5d8Riex441y+n3CJE9SBnwn32W3ee77/v8b7ZI7oP4QqmSU+MYFef5vFDjvUnDOjXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61d2fb75e7861c6112a1b13ad8f0d3491d59e47cd557b6ff0301a5fc61bb40e7","last_reissued_at":"2026-05-18T00:42:40.478896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:40.478896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lie-Type Derivations of Nest Algebras on Banach Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RA"],"primary_cat":"math.FA","authors_text":"Feng Wei, Yuhao Zhang","submitted_at":"2017-06-09T13:54:15Z","abstract_excerpt":"Let $\\mathcal{X}$ be a Banach space over the complex field $\\mathbb{C}$ and $\\mathcal{B(X)}$ be the algebra of all bounded linear operators on $\\mathcal{X}$. Let $\\mathcal{N}$ be a non-trivial nest on $\\mathcal{X}$, ${\\rm Alg}\\mathcal{N}$ be the nest algebra associated with $\\mathcal{N}$, and $L\\colon {\\rm Alg}\\mathcal{N}\\longrightarrow \\mathcal{B(X)}$ be a linear mapping. Suppose that $p_n(x_1,x_2,\\cdots,x_n)$ is an $(n-1)$-th commutator defined by $n$ indeterminates $x_1, x_2, \\cdots, x_n$. It is shown that $L$ satisfies the rule $$ L(p_n(A_1, A_2, \\cdots, A_n))=\\sum_{k=1}^{n}p_n(A_1, \\cdots"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02951","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":"1706.02951","created_at":"2026-05-18T00:42:40.478980+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.02951v1","created_at":"2026-05-18T00:42:40.478980+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02951","created_at":"2026-05-18T00:42:40.478980+00:00"},{"alias_kind":"pith_short_12","alias_value":"MHJPW5PHQYOG","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MHJPW5PHQYOGCEVB","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MHJPW5PH","created_at":"2026-05-18T12:31:31.346846+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/MHJPW5PHQYOGCEVBWE5NR4GTJE","json":"https://pith.science/pith/MHJPW5PHQYOGCEVBWE5NR4GTJE.json","graph_json":"https://pith.science/api/pith-number/MHJPW5PHQYOGCEVBWE5NR4GTJE/graph.json","events_json":"https://pith.science/api/pith-number/MHJPW5PHQYOGCEVBWE5NR4GTJE/events.json","paper":"https://pith.science/paper/MHJPW5PH"},"agent_actions":{"view_html":"https://pith.science/pith/MHJPW5PHQYOGCEVBWE5NR4GTJE","download_json":"https://pith.science/pith/MHJPW5PHQYOGCEVBWE5NR4GTJE.json","view_paper":"https://pith.science/paper/MHJPW5PH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.02951&json=true","fetch_graph":"https://pith.science/api/pith-number/MHJPW5PHQYOGCEVBWE5NR4GTJE/graph.json","fetch_events":"https://pith.science/api/pith-number/MHJPW5PHQYOGCEVBWE5NR4GTJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MHJPW5PHQYOGCEVBWE5NR4GTJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MHJPW5PHQYOGCEVBWE5NR4GTJE/action/storage_attestation","attest_author":"https://pith.science/pith/MHJPW5PHQYOGCEVBWE5NR4GTJE/action/author_attestation","sign_citation":"https://pith.science/pith/MHJPW5PHQYOGCEVBWE5NR4GTJE/action/citation_signature","submit_replication":"https://pith.science/pith/MHJPW5PHQYOGCEVBWE5NR4GTJE/action/replication_record"}},"created_at":"2026-05-18T00:42:40.478980+00:00","updated_at":"2026-05-18T00:42:40.478980+00:00"}