{"paper":{"title":"An extension of Haagerup's reduction theorem with applications to subdiagonal subalgebras of general von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Louis Labuschagne, Quanhua Xu","submitted_at":"2025-06-07T05:52:37Z","abstract_excerpt":"We revisit Haagerup's enigmatic reduction theorem \\cite[Theorems 2.1 \\& 3.1]{HJX} showing how that theorem may be extended to general von Neumann algebras $\\M$ equipped with an arbitrary faithful normal semifinite weight in a manner which faithfully captures the essence of the original. In contrast to the proposal in \\cite[Remark 2.8]{HJX}, we show how in the non-$\\sigma$-finite case the enlargement $\\R=\\M\\rtimes\\mathbb{Q}_D$ of $\\M$ may be approximated by an increasing \\emph{sequence} of \\emph{expected} semifinite subalgebras. Using this revised version of the reduction theorem we may then al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06674","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.06674/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}