{"paper":{"title":"On realization of generalized effect algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.RT","authors_text":"Jan Paseka","submitted_at":"2012-08-07T15:48:21Z","abstract_excerpt":"A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice $L({\\mathcal H})$ of all closed subspaces of a separable complex Hilbert space.\n  We show that a generalized effect algebra is representable in the operator generalized effect algebra ${\\mathcal G}_D({\\mathcal H})$ of effects of a complex Hilbert space ${\\mathcal H}$ iff it has an order determining set of generalized states.\n  This extends the corresponding results for effect algebras of Rie\\v{c}anov\\'a and Zajac. Further"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1450","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"}