{"paper":{"title":"Functions of perturbed $n$-tuples of 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":"Fyodor Nazarov, Vladimir Peller","submitted_at":"2013-08-23T14:53:42Z","abstract_excerpt":"Let $(A_1,\\cdots,A_n)$ and $(B_1,\\cdots,B_n)$ be $n$-tuples of commuting self-adjoint operators on Hilbert space. For functions $f$ on $\\R^n$ satisfying certain conditions, we obtain sharp estimates of the operator norms (or norms in operator ideals) of $f(A_1,\\cdots,A_n)-f(B_1,\\cdots,B_n)$ in terms of the corresponding norms of $A_j-B_j$, $1\\le j\\le n$.\n  We obtain analogs of earlier results on estimates for functions of perturbed self-adjoint and normal operators. It turns out that for $n\\ge3$, the methods that were used for self-adjoint and normal operators do not work. We propose a new met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5147","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"}