{"paper":{"title":"Intersecting Jones projections","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Sebastiano Carpi","submitted_at":"2004-12-22T15:55:28Z","abstract_excerpt":"Let M be a von Neumann algebra on a Hilbert space H with a cyclic and separating unit vector \\Omega and let \\omega be the faithful normal state on M given by \\omega(\\cdot)=(\\Omega,\\cdot\\Omega). Moreover, let {N_i :i\\in I} be a family of von Neumann subalgebras of M with faithful normal conditional expectations E_i of M onto N_i satisfying \\omega=\\omega\\circ E_i for all i\\in I and let N=\\bigcap_{i\\in I} N_i. We show that the projections e_i, e of H onto the closed subspaces \\bar{N_i\\Omega} and \\bar{N\\Omega} respectively satisfy e=\\bigwedge_{i\\in I}e_i.This proves a conjecture of V.F.R. Jones an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412457","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"}