{"paper":{"title":"Locally quasi-nilpotent elementary operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RA","authors_text":"Martin Mathieu, Nadia Boudi","submitted_at":"2013-02-27T11:46:07Z","abstract_excerpt":"Let $A$ be a unital dense algebra of linear mappings on a complex vector space $X$. Let $\\phi=\\sum_{i=1}^n M_{a_i,b_i}$ be a locally quasi-nilpotent elementary operator of length $n$ on $A$. We show that, if $\\{a_1,\\ldots,a_n\\}$ is locally linearly independent, then the local dimension of $V(\\phi)=\\spa\\{b_ia_j: 1 \\leq i,j \\leq n\\}$ is at most $\\frac{n(n-1)}{2}$. If $\\lDim V(\\phi)=\\frac{n(n-1)}{2} $, then there exists a representation of $\\phi$ as $\\phi=\\sum_{i=1}^n M_{u_i,v_i}$ with $v_iu_j=0$ for $i\\geq j$. Moreover, we give a complete characterization of locally quasi-nilpotent elementary op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6735","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"}