{"paper":{"title":"On a spectral flow formula for the homological index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alan Carey, Harald Grosse, Jens Kaad","submitted_at":"2015-01-22T10:48:48Z","abstract_excerpt":"Consider a selfadjoint unbounded operator D on a Hilbert space H and a one parameter norm continuous family of selfadjoint bounded operators {A(t)} parametrized by the real line. Then under certain conditions \\cite{RS95} that include the assumption that the operators {D(t)= D+A(t)} all have discrete spectrum then the spectral flow along the path { D(t)} can be shown to be equal to the index of d/dt+D(t) when the latter is an unbounded Fredholm operator on L^2(R, H). In \\cite{GLMST11} an investigation of the index=spectral flow question when the operators in the path may have some essential spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05453","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"}