{"paper":{"title":"Almost commuting functions of almost commuting self-adjoint operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Aleksei Aleksandrov, Vladimir Peller","submitted_at":"2014-12-11T04:29:57Z","abstract_excerpt":"Let $A$ and $B$ be almost commuting (i.e, $AB-BA\\in\\bS_1$) self-adjoint operators. We construct a functional calculus $\\f\\mapsto\\f(A,B)$ for $\\f$ in the Besov class $B_{\\be,1}^1(\\R^2)$. This functional calculus is linear, the operators $\\f(A,B)$ and $\\psi(A,B)$ almost commute for $\\f,\\,\\psi\\in B_{\\be,1}^1(\\R^2)$, $\\f(A,B)=u(A)v(B)$ whenever $\\f(s,t)=u(s)v(t)$, and the Helton--Howe trace formula holds. The main tool is triple operator integrals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3535","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"}