{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:RT47UTBEX6V4NU4IK24KIGZV3V","short_pith_number":"pith:RT47UTBE","schema_version":"1.0","canonical_sha256":"8cf9fa4c24bfabc6d38856b8a41b35dd796a4933ef8980d5519757f05fed6c56","source":{"kind":"arxiv","id":"math/0412457","version":1},"attestation_state":"computed","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. 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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. 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