{"paper":{"title":"Characterizing derivations for any nest algebras on Banach spaces by their behaviors at an injective operator","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Jinchuan Hou, Xiaofei Qi, Yanfang Zhang","submitted_at":"2013-11-21T00:23:59Z","abstract_excerpt":"Let ${\\mathcal N}$ be a nest on a complex Banach space $X$ and let $\\mbox{ Alg}{\\mathcal N}$ be the associated nest algebra. We say that an operator $Z\\in \\mbox{ Alg}{\\mathcal N}$ is an all-derivable point of $\\mbox{ Alg}{\\mathcal N}$ if every linear map $\\delta$ from $\\mbox{ Alg}{\\mathcal N}$ into itself derivable at $Z$ (i.e. $\\delta$ satisfies $\\delta(A)B+A\\delta(B)=\\delta(Z)$ for any $A,B \\in \\mbox{ Alg}{\\mathcal N}$ with $AB=Z$) is a derivation. In this paper, it is shown that every injective operator and every operator with dense range in $\\mbox{Alg}{\\mathcal N}$ are all-derivable points"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5276","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"}