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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.6735","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-02-27T11:46:07Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"08091cca52fd0538e6667fca4af36f3bf7a31d917311f2e1491e0a6a5258e18d","abstract_canon_sha256":"706199f7650ea471bbf534c59bde1bd4dbfb6d02f3ecb35d0a7996545081802c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:15.473504Z","signature_b64":"WfWyKoJcAj+annSP7F2tPyvKPQMv5p5mq2oJfFLhYjXBtD/3wZe1wl5Q5A/djyaLY/Y9kklxLiYrvC7P05p1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5f75c41fabd30a9c66f50bde51ffae2e4155357a979c436b52710a06d8bb1e0","last_reissued_at":"2026-05-18T03:04:15.472816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:15.472816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $i\\geq j$. 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