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If $\\vee\\{L\\in \\mathcal{L}: L_-\\nsupseteq L\\}=X$ or $\\wedge\\{L_-:L\\in \\mathcal{L}, L_-\\nsupseteq L\\}=(0)$, we show that the following three conditions are equivalent: (1) $\\delta(AB)=\\delta(A)B+A\\delta(B)$ whenever $AB=0$; (2) $\\delta(AB+BA)=\\delta(A)B+A\\delta(B)+\\delta(B)A+B\\delta(A)$ whenever $AB+BA=0$; (3) $\\delta$ is a generalized derivation and $\\delta(I)\\in (\\mathrm{Alg}\\mathcal{L})^\\prime$. If $\\vee\\{L\\in \\mathcal{L}: L_-\\nsupseteq L\\}=X$ or $\\wedge"},"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":"1106.4371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-22T05:23:31Z","cross_cats_sorted":[],"title_canon_sha256":"deb5a7c52d2634c8af56c17c7d2647a7e768f07a59e08d7d3a8215aa253abc5b","abstract_canon_sha256":"653d00fdb03c2169865c585c5899e75f2c26bf1e966cfb36bf9f76a125b9bb33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:33.084205Z","signature_b64":"9wk9ia8aVl2cWLfZ8POm9LzVqXTgAkmEEGYYQE612525LWqL9b2X/Wx81v35qlkVTcjOkOWJtFRDsRCLBpbEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49d9e98c69154113b17593666a3e0dfa3d3a7af2e0500470735d6f0c599825fa","last_reissued_at":"2026-05-18T04:19:33.083746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:33.083746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jiankui Li, Yunhe Chen","submitted_at":"2011-06-22T05:23:31Z","abstract_excerpt":"Let $\\mathcal{L}$ be a subspace lattice on a Banach space $X$ and let $\\delta:\\mathrm{Alg}\\mathcal{L}\\rightarrow B(X)$ be a linear mapping. If $\\vee\\{L\\in \\mathcal{L}: L_-\\nsupseteq L\\}=X$ or $\\wedge\\{L_-:L\\in \\mathcal{L}, L_-\\nsupseteq L\\}=(0)$, we show that the following three conditions are equivalent: (1) $\\delta(AB)=\\delta(A)B+A\\delta(B)$ whenever $AB=0$; (2) $\\delta(AB+BA)=\\delta(A)B+A\\delta(B)+\\delta(B)A+B\\delta(A)$ whenever $AB+BA=0$; (3) $\\delta$ is a generalized derivation and $\\delta(I)\\in (\\mathrm{Alg}\\mathcal{L})^\\prime$. 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