{"paper":{"title":"A quantitative version of the commutator theorem for zero trace matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gideon Schechtman, Narutaka Ozawa, William B. Johnson","submitted_at":"2012-02-05T18:16:14Z","abstract_excerpt":"Let $A$ be a $m\\times m$ complex matrix with zero trace and let $\\e>0$. Then there are $m\\times m$ matrices $B$ and $C$ such that $A=[B,C]$ and $\\|B\\|\\|C\\|\\le K_\\e m^\\e\\|A\\|$ where $K_\\e$ depends only on $\\e$. Moreover, the matrix $B$ can be taken to be normal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0986","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"}