{"paper":{"title":"On the difference of spectral projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Christoph Uebersohn","submitted_at":"2014-06-25T10:09:50Z","abstract_excerpt":"For a semibounded self-adjoint operator $ T $ and a compact self-adjoint operator $ S $ acting on a complex separable Hilbert space of infinite dimension, we study the difference $ D(\\lambda) := E_{(-\\infty, \\lambda)}(T+S) - E_{(-\\infty, \\lambda)}(T), \\, \\lambda \\in \\mathbb{R} $, of the spectral projections associated with the open interval $ (-\\infty, \\lambda) $.\n  In the case when $ S $ is of rank one, we show that $ D(\\lambda) $ is unitarily equivalent to a block diagonal operator $ \\Gamma_{\\lambda} \\oplus 0 $, where $ \\Gamma_{\\lambda} $ is a bounded self-adjoint Hankel operator, for all $ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6516","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"}