{"paper":{"title":"On the Index of a Non-Fredholm Model Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alan Carey, Fedor Sukochev, Fritz Gesztesy, Galina Levitina","submitted_at":"2015-09-04T08:39:09Z","abstract_excerpt":"Let $\\{A(t)\\}_{t \\in \\mathbb{R}}$ be a path of self-adjoint Fredholm operators in a Hilbert space $\\mathcal{H}$, joining endpoints $A_\\pm$ as $t \\to \\pm \\infty$. Computing the index of the operator $D_A= (d/d t) + A$ acting in $L^2(\\mathbb{R}; \\mathcal{H})$, where $A = \\int_{\\mathbb{R}}^{\\oplus} dt \\, A(t)$, and its relation to spectral flow along this path, has a long history. While most of the latter focuses on the case where $A(t)$ all have purely discrete spectrum, we now particularly study situations permitting essential spectra.\n  Introducing $H_1={D_A}^* D_A$ and $H_2=D_A {D_A}^*$, we c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01580","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"}