{"paper":{"title":"Maximal left ideals of the Banach algebra of bounded operators on a Banach space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"H. G. Dales, Niels Jakob Laustsen, Piotr Koszmider, Tomasz Kania, Tomasz Kochanek","submitted_at":"2012-08-23T14:13:06Z","abstract_excerpt":"We address the following two questions regarding the maximal left ideals of the Banach algebra $\\mathscr{B}(E)$ of bounded operators acting on an infinite-dimensional Banach pace $E$:\n  (Q1) Does $\\mathscr{B}(E)$ always contain a maximal left ideal which is not finitely generated? (Q2) Is every finitely-generated, maximal left ideal of $\\mathscr{B}(E)$ necessarily of the form \\{T\\in\\mathscr{B}(E): Tx = 0\\} (*) for some non-zero $x\\in E$?\n  Since the two-sided ideal $\\mathscr{F}(E)$ of finite-rank operators is not contained in any of the maximal left ideals given by (*), a positive answer to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4762","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"}