{"paper":{"title":"Ideal structure of the algebra of bounded operators acting on a Banach space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.FA","authors_text":"Niels Jakob Laustsen, Tomasz Kania","submitted_at":"2015-07-05T12:31:05Z","abstract_excerpt":"We construct a Banach space $Z$ such that the lattice of closed two-sided ideals of the Banach algebra $\\mathscr{B}(Z)$ of bounded operators on $Z$ is as follows: $$ \\{0\\}\\subset \\mathscr{K}(Z)\\subset\\mathscr{E}(Z)\n  \\raisebox{-.5ex}%\n  {\\ensuremath{\\overset{\\begin{turn}{30}$\\subset$\\end{turn}}%\n  {\\begin{turn}{-30}$\\subset$\\end{turn}}}}\\!\\!%\n  \\begin{array}{c}\\mathscr{M}_1\\\\[1mm]\\mathscr{M}_2\\end{array}\\!\\!\\!%\n  \\raisebox{-1.25ex}%\n  {\\ensuremath{\\overset{\\raisebox{1.25ex}{\\ensuremath{\\begin{turn}{-30}$\\subset$\\end{turn}}}}%\n  {\\raisebox{-.25ex}{\\ensuremath{\\begin{turn}{30}$\\subset$\\end{turn}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01213","kind":"arxiv","version":2},"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"}