{"paper":{"title":"Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"H. Neidhardt, M.M. Malamud, V.V. Peller","submitted_at":"2017-05-19T23:49:48Z","abstract_excerpt":"In this paper we prove that for an arbitrary pair $\\{T_1,T_0\\}$ of contractions on Hilbert space with trace class difference, there exists a function $\\boldsymbol\\xi$ in $L^1({\\Bbb T})$ (called a spectral shift function for the pair $\\{T_1,T_0\\}$ ) such that the trace formula $\\operatorname{trace}(f(T_1)-f(T_0))=\\int_{\\Bbb T} f'(\\zeta)\\boldsymbol{\\xi}(\\zeta)\\,d\\zeta$) holds for an arbitrary operator Lipschitz function $f$ analytic in the unit disk."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07225","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"}