{"paper":{"title":"On the invertibility of elementary operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Janko Bra\\v{c}i\\v{c}, Nadia Boudi","submitted_at":"2013-12-04T20:06:42Z","abstract_excerpt":"Let $\\mathscr{X}$ be a complex Banach space and $\\mathcal{L}(\\mathscr{X})$ be the algebra of all bounded linear operators on $\\mathscr{X}$. For a given elementary operator $\\Phi$ of length $2$ on $\\mathcal{L}(\\mathscr{X})$, we determine necessary and sufficient conditions for the existence of a solution of the equation ${\\rm X} \\Phi=0$ in the algebra of all elementary operators on $\\mathcal{L}(\\mathscr{X})$. Our approach allows us to characterize some invertible elementary operators of length $2$ whose inverses are elementary operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1307","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"}