{"paper":{"title":"The Uniqueness Problem of Sequence Product on Operator Effect Algebra $\\varepsilon (H)$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP","math.OA","math.QA","quant-ph"],"primary_cat":"math-ph","authors_text":"Liu Weihua, Wu Junde","submitted_at":"2008-12-03T01:28:15Z","abstract_excerpt":"A quantum effect is an operator on a complex Hilbert space $H$ that satisfies $0\\leq A\\leq I$. We denote the set of all quantum effects by ${\\cal E}(H)$. In this paper we prove, Theorem 4.3, on the theory of sequential product on ${\\cal E}(H)$ which shows, in fact, that there are sequential products on ${\\cal E}(H)$ which are not of the generalized L\\\"{u}ders form. This result answers a Gudder's open problem negatively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0630","kind":"arxiv","version":3},"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"}