{"paper":{"title":"Partially fundamentally reducible operators in Krein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Branko \\'Curgus, Vladimir Derkach","submitted_at":"2014-07-26T08:25:20Z","abstract_excerpt":"A self-adjoint operator $A$ in a Krein space $\\bigl({\\mathcal K},[\\,\\cdot\\,,\\cdot\\,]\\bigr)$ is called partially fundamentally reducible if there exist a fundamental decomposition ${\\mathcal K} = {\\mathcal K}_+ [\\dot{+}] {\\mathcal K}_-$ (which does not reduce $A$) and densely defined symmetric operators $S_+$ and $S_-$ in the Hilbert spaces $\\bigl({\\mathcal K}_+,[\\,\\cdot\\,,\\cdot\\,]\\bigr)$ and $\\bigl({\\mathcal K}_-,-[\\,\\cdot\\,,\\cdot\\,]\\bigr)$, respectively, such that each $S_+$ and $S_-$ has defect numbers $(1,1)$ and the operator $A$ is a self-adjoint extension of $S =S_+ \\oplus (-S_-)$ in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7108","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"}