{"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"}