{"paper":{"title":"Functions of almost commuting operators and an extension of the Helton-Howe trace formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Alexei Aleksandrov, Vladimir Peller","submitted_at":"2015-08-19T16:44:42Z","abstract_excerpt":"Let $A$ and $B$ be almost commuting (i.e., the commutator $AB-BA$ belongs to trace class) self-adjoint operators. We construct a functional calculus $\\varphi\\mapsto\\varphi(A,B)$ for functions $\\varphi$ in the Besov class $B_{\\infty,1}^1({\\Bbb R}^2)$. This functional calculus is linear, the operators $\\varphi(A,B)$ and $\\psi(A,B)$ almost commute for $\\varphi,\\,\\psi\\in B_{\\infty,1}^1({\\Bbb R}^2)$, and $\\varphi(A,B)=u(A)v(B)$ whenever $\\varphi(s,t)=u(s)v(t)$. We extend the Helton--Howe trace formula for arbitrary functions in $B_{\\infty,1}^1({\\Bbb R}^2)$. The main tool is triple operator integral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04702","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"}