{"paper":{"title":"On the Witten index in terms of spectral shift functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Alan Carey, Denis Potapov, Fedor Sukochev, Fritz Gesztesy, Yuri Tomilov","submitted_at":"2014-04-03T00:48:24Z","abstract_excerpt":"We study the model operator $\\mathbf{D}_{\\mathbf{A}} = (d/dt) + \\mathbf{A}$ in $L^2(\\mathbb{R};\\mathcal{H})$ associated with the operator path $\\{A(t)\\}_{t=-\\infty}^{\\infty}$, where $(\\mathbf{A} f)(t) = A(t) f(t)$ for a.e.\\ $t\\in\\mathbb{R}$, and appropriate $f \\in L^2(\\mathbb{R};\\mathcal{H})$ (with $\\mathcal{H}$ a separable, complex Hilbert space). Denoting by $A_{\\pm}$ the norm resolvent limits of $A(t)$ as $t \\to \\pm \\infty$, our setup permits $A(t)$ in $\\mathcal{H}$ to be an unbounded, relatively trace class perturbation of the unbounded self-adjoint operator $A_-$, and no discrete spectrum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0740","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"}