{"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 $\\delta(I)\\in (\\mathrm{Alg}\\mathcal{L})^\\prime$. If $\\vee\\{L\\in \\mathcal{L}: L_-\\nsupseteq L\\}=X$ or $\\wedge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4371","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"}