{"paper":{"title":"On Commuting and Semi-commuting Positive Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Niushan Gao","submitted_at":"2012-08-16T21:26:40Z","abstract_excerpt":"Let $K$ be a positive compact operator on a Banach lattice. We prove that if either $[K>$ or $<K]$ is ideal irreducible then $[K>=<K]=L_+(X)\\cap {K}'$. We also establish the Perron-Frobenius Theorem for such operators $K$. Finally we apply the results to answer questions in Abramovich and Aliprantis (2002) and Bra\\v{c}i\\v{c} (2010)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3495","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"}