{"paper":{"title":"Functions of noncommuting self-adjoint operators under perturbation and estimates of triple operator integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.B. Aleksandrov, F.L. Nazarov, V.V. Peller","submitted_at":"2015-05-27T02:10:16Z","abstract_excerpt":"We define functions of noncommuting self-adjoint operators with the help of double operator integrals. We are studying the problem to find conditions on a function $f$ on ${\\Bbb R}^2$, for which the map $(A,B)\\mapsto f(A,B)$ is Lipschitz in the operator norm and in Schatten--von Neumann norms $\\boldsymbol{S}_p$. It turns out that for functions $f$ in the Besov class $B_{\\infty,1}^1({\\Bbb R}^2)$, the above map is Lipschitz in the $\\boldsymbol{S}_p$ norm for $p\\in[1,2]$. However, it is not Lipschitz in the operator norm, nor in the $\\boldsymbol{S}_p$ norm for $p>2$. The main tool is triple opera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07173","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"}