{"paper":{"title":"All-derivable points in nest algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Wu Junde, Zhang Lin, Zhu Jun","submitted_at":"2010-08-09T00:35:04Z","abstract_excerpt":"Suppose that $\\mathscr{A}$ is an operator algebra on a Hilbert space $H$. An element $V$ in $\\mathscr{A}$ is called an all-derivable point of $\\mathscr{A}$ for the strong operator topology if every strong operator topology continuous derivable mapping $\\phi$ at $V$ is a derivation. Let $\\mathscr{N}$ be a complete nest on a complex and separable Hilbert space $H$. Suppose that $M$ belongs to $\\mathscr{N}$ with $\\{0\\}\\neq M\\neq\\ H$ and write $\\hat{M}$ for $M$ or $M^{\\bot}$. Our main result is: for any $\\Omega\\in alg\\mathscr{N}$ with $\\Omega=P(\\hat{M})\\Omega P(\\hat{M})$, if $\\Omega |_{\\hat{M}}$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1434","kind":"arxiv","version":3},"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"}