{"paper":{"title":"Reducible and irreducible approximation of complex symmetric operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Jiayin Zhao, Sen Zhu, Ting Liu","submitted_at":"2018-12-11T22:39:47Z","abstract_excerpt":"This paper aims to study reducible and irreducible approximation in the set $\\textsl{CSO}$ of all complex symmetric operators on a separable, complex Hilbert space $\\mathcal H$. When ${\\rm dim} \\mathcal H=\\infty$, it is proved that both those reducible ones and those irreducible ones are norm dense in $\\textsl{CSO}$. When ${\\rm dim} \\mathcal H<\\infty$, irreducible complex symmetric operators constitute an open, dense subset of $\\textsl{CSO}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04733","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"}