{"paper":{"title":"Sequential product on standard effect algebra ${\\cal E} (H)$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Shen Jun, Wu Junde","submitted_at":"2009-05-05T12:50:13Z","abstract_excerpt":"A quantum effect is an operator $A$ on a complex Hilbert space $H$ that satisfies $0\\leq A\\leq I$, ${\\cal E} (H)$ is the set of all quantum effects on $H$. In 2001, Professor Gudder and Nagy studied the sequential product $A\\circ B=A^{{1/2}}BA^{{1/2}}$ of $A, B\\in {\\cal E}(H)$. In 2005, Professor Gudder asked: Is $A\\circ B=A^{{1/2}}BA^{{1/2}}$ the only sequential product on ${\\cal E} (H)$? Recently, Liu and Wu presented an example to show that the answer is negative. In this paper, firstly, we characterize some algebraic properties of the abstract sequential product on ${\\cal E} (H)$; secondly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0596","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"}