{"paper":{"title":"Triple operator integrals in Schatten--von Neumann norms and functions of perturbed noncommuting 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, Fedor Nazarov, Vladimir Peller","submitted_at":"2015-04-06T02:30:26Z","abstract_excerpt":"We study perturbations of functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and $B$ that can be defined in terms of double operator integrals. We prove that if $f$ belongs to the Besov class $B_{\\be,1}^1(\\R^2)$, then we have the following Lipschitz type estimate in the Schatten--von Neumann norm $\\bS_p$, $1\\le p\\le2$ norm: $\\|f(A_1,B_1)-f(A_2,B_2)\\|_{\\bS_p}\\le\\const(\\|A_1-A_2\\|_{\\bS_p}+\\|B_1-B_2\\|_{\\bS_p})$. However, the condition $f\\in B_{\\be,1}^1(\\R^2)$ does not imply the Lipschitz type estimate in $\\bS_p$ with $p>2$. The main tool is Schatten--von Neumann norm estimates for trip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01189","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"}