{"paper":{"title":"Characterizations of all-derivable points in nest algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jun Zhu, Sha Zhao","submitted_at":"2011-07-11T03:49:17Z","abstract_excerpt":"Let $\\mathcal{A}$ be an operator algebra on a Hilbert space. We say that an element $G\\in {\\mathcal{A}}$ is an all-derivable point of ${\\mathcal{A}}$ if every derivable linear mapping $\\phi$ at $G$ (i.e. $\\phi(ST)=\\phi(S)T+S\\phi(T)$ for any $S,T\\in alg{\\mathcal{N}}$ with $ST=G$) is a derivation. Suppose that $\\mathcal{N}$ is a nontrivial complete nest on a Hilbert space $H$. We show in this paper that $G\\in {alg\\mathcal{N}}$ is an all-derivable point if and only if $G\\neq0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1931","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"}