{"paper":{"title":"Weakly closed Lie modules of nest algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Lina Oliveira, Miguel Santos","submitted_at":"2015-12-10T20:43:44Z","abstract_excerpt":"Let $\\mathcal{T}(\\mathcal{N})$ be a nest algebra of operators on Hilbert space and let $\\mathcal{L}$ be a weakly closed Lie $\\mathcal{T}(\\mathcal{N})$-module. We construct explicitly the largest possible weakly closed $\\mathcal{T}(\\mathcal{N})$-bimodule $\\mathcal{J}(\\mathcal{L})$ and a weakly closed $\\mathcal{T}(\\mathcal{N})$-bimodule $\\mathcal{K}(\\mathcal{L})$ such that \\[ \\mathcal{J}(\\mathcal{L})\\subseteq \\mathcal{L} \\subseteq \\mathcal{K}(\\mathcal{L}) +\\mathcal{D}_{\\mathcal{K}(\\mathcal{L})}, \\]\n  $[\\mathcal{K}(\\mathcal{L}), \\mathcal{T}(\\mathcal{N})]\\subseteq \\mathcal{L}$ and $\\mathcal{D}_{\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03408","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"}