{"paper":{"title":"Commutator estimates in $W^*$-factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"A. F. Ber, F. A. Sukochev","submitted_at":"2010-08-19T04:41:24Z","abstract_excerpt":"Let $\\mathcal{M}$ be a $W^*$-factor and let $S\\left( \\mathcal{M} \\right) $ be the space of all measurable operators affiliated with $\\mathcal{M}$. It is shown that for any self-adjoint element $a\\in S(\\mathcal{M})$ there exists a scalar $\\lambda_0\\in\\mathbb{R}$, such that for all $\\varepsilon > 0$, there exists a unitary element $u_\\varepsilon$ from $\\mathcal{M}$, satisfying $|[a,u_\\varepsilon]| \\geq (1-\\varepsilon)|a-\\lambda_0\\mathbf{1}|$. A corollary of this result is that for any derivation $\\delta$ on $\\mathcal{M}$ with the range in an ideal $I\\subseteq\\mathcal{M}$, the derivation $\\delta$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3210","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"}