{"paper":{"title":"Functions of normal operators under perturbations","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, Denis Potapov, Fedor Sukochev, Vladimir Peller","submitted_at":"2010-08-10T06:08:52Z","abstract_excerpt":"In \\cite{Pe1}, \\cite{Pe2}, \\cite{AP1}, \\cite{AP2}, and \\cite{AP3} sharp estimates for $f(A)-f(B)$ were obtained for self-adjoint operators $A$ and $B$ and for various classes of functions $f$ on the real line $\\R$. In this paper we extend those results to the case of functions of normal operators. We show that if a function $f$ belongs to the H\\\"older class $\\L_\\a(\\R^2)$, $0<\\a<1$, of functions of two variables, and $N_1$ and $N_2$ are normal operators, then $\\|f(N_1)-f(N_2)\\|\\le\\const\\|f\\|_{\\L_\\a}\\|N_1-N_2\\|^\\a$. We obtain a more general result for functions in the space $\\L_\\o(\\R^2)=\\big\\{f:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1638","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"}