{"paper":{"title":"Double operator integral methods applied to continuity of spectral shift functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Alan Carey, Denis Potapov, Fedor Sukochev, Fritz Gesztesy, Galina Levitina, Roger Nichols","submitted_at":"2015-11-25T09:16:59Z","abstract_excerpt":"We derive two main results: First, assume that $A$, $B$, $A_n$, $B_n$ are self-adjoint operators in the Hilbert space $\\mathcal{H}$, and suppose that $A_n$ converges to $A$ and $B_n$ to $B$ in strong resolvent sense as $n \\to \\infty$. Fix $m \\in \\mathbb{N}$, $m$ odd, $p \\in [1,\\infty)$, and assume that $T:= \\big[( A + iI_{\\mathcal{H}})^{-m} - ( B + iI_{\\mathcal{H}})^{-m}\\big] \\in \\mathcal{B}_p(\\mathcal{H})$, $T_n := \\big[( A_n + iI_{\\mathcal{H}})^{-m} - ( B_n + iI_{\\mathcal{H}})^{-m}\\big] \\in \\mathcal{B}_p(\\mathcal{H})$, and $\\lim_{n \\rightarrow \\infty} \\|T_n - T\\|_{\\mathcal{B}_p(\\mathcal{H})}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07998","kind":"arxiv","version":2},"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"}