{"paper":{"title":"Sharpening the norm bound in the subspace perturbation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Alexander K. Motovilov, Sergio Albeverio","submitted_at":"2011-12-01T11:59:52Z","abstract_excerpt":"Let A be a self-adjoint operator on a Hilbert space H. Assume that {\\sigma} is an isolated component of the spectrum of A, i.e. dist({\\sigma},{\\Sigma})=d>0 where {\\Sigma}=spec(A)\\{\\sigma}. Suppose that V is a bounded self-adjoint operator on H such that ||V||<d/2 and let L=A+V. Denote by P the spectral projection of A associated with the spectral set {\\sigma} and let Q be the spectral projection of L corresponding to the closed ||V||-neighborhood of {\\sigma}. We prove a bound of the form arcsin(||P-Q||)\\leq M(||V||/d), M: [0,1/2)-->R^+, that is essentially stronger than the previously known es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0149","kind":"arxiv","version":3},"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"}