{"paper":{"title":"The index formula and the spectral shift function for relatively trace class perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Fedor Sukochev, Fritz Gesztesy, Konstantin A. Makarov, Yuri Latushkin, Yuri Tomilov","submitted_at":"2010-04-09T15:54:13Z","abstract_excerpt":"We compute the Fredholm index, ${\\rm ind}(D_A)$, of the operator $D_A = (d/dt) + A$ on $L^2(\\mathbb{R};\\mathcal{H})$ associated with the operator path $\\{A(t)\\}_{t=-\\infty}^{\\infty}$, where $(A f)(t) = A(t) f(t)$ for a.e. $t\\in\\mathbb{R}$, and appropriate $f \\in L^2(\\mathbb{R};\\mathcal{H})$, via the spectral shift function $\\xi(\\, \\cdot \\,;A_+,A_-)$ associated with the pair $(A_+, A_-)$ of asymptotic operators $A_{\\pm}=A(\\pm\\infty)$ on the separable complex Hilbert space $\\mathcal{H}$ in the case when $A(t)$ is generally an unbounded (relatively trace class) perturbation of the unbounded self-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1582","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"}