{"paper":{"title":"Functions of triples of noncommuting self-adjoint operators under perturbations of class $\\boldsymbol S_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"V.V. Peller","submitted_at":"2017-05-19T23:59:27Z","abstract_excerpt":"In this paper we study properties of functions of triples of not necessarily commuting self-adjoint operators. The main result of the paper shows that unlike in the case of functions of pairs of self-adjoint operators there is no Lipschitz type estimates in any Schatten--von Neumann norm $\\boldsymbol S_p$, $1\\le p\\le\\infty$, for arbitrary functions in the Besov class $B_{\\infty,1}^1({\\Bbb R}^3)$. In other words, we prove that for $p\\in[1,\\infty]$, there is no constant $K>0$ such that the inequality \\begin{align*} \\|f(A_1,B_1,C_1)&-f(A_2,B_2,C_2)\\|_{\\boldsymbol S_p}\\\\[.1cm] &\\le K\\|f\\|_{B_{\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01969","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"}