{"paper":{"title":"On (m,n,l)-Jordan Centralizers of Some Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jianbin Guo, Jiankui Li, Qihua Shen","submitted_at":"2011-05-30T12:57:54Z","abstract_excerpt":"Let $\\mathcal{A}$ be a unital algebra over the complex field $\\mathbb{C}$. A linear mapping $\\delta$ from $\\mathcal{A}$ into itself is called a weak (\\textit{m,n,l})-Jordan centralizer if $(m+n+l)\\delta(A^2)-m\\delta(A)A-nA\\delta(A)-lA\\delta(I)A\\in \\mathbb{C}I$ for every $A\\in \\mathcal{A}$, where $m\\geq0, n\\geq0, l\\geq0$ are fixed integers with $m+n+l\\neq 0$. In this paper, we study weak (\\textit{m,n,l})-Jordan centralizer on generalized matrix algebras and some reflexive algebras alg$\\mathcal{L}$, where $\\mathcal{L}$ is CSL or satisfies $\\vee\\{L: L\\in \\mathcal{J}(\\mathcal{L})\\}=X$ or $\\wedge\\{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5976","kind":"arxiv","version":2},"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"}