{"id":"W4288622741","doi":"10.48550/arxiv.1901.08700","title":"A non-commutative Fej\\\\'{e}r theorem for crossed products, the\\n approximation property, and applications","year":2019,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Locally compact space; Mathematics; Fubini's theorem; Pure mathematics; Commutative property; Von Neumann architecture; Approximation property; Locally compact group; Group (periodic table); Property (philosophy); Dynamical systems theory; Product (mathematics); Banach space; Crossed product; Discrete mathematics; Algebra over a field; Quantum mechanics; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006587345,0.0003460092,0.0004127308,0.0001376142,0.0004316686,0.0001483987,0.0008601646,0.0002339963,0.0000131046],"category_scores_gemma":[0.0003487031,0.0002432105,0.0001173124,0.0004018343,0.0004257007,0.0002257053,0.001027037,0.0006704669,0.00003565717],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002145477,"about_ca_system_score_gemma":0.0003136946,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000240152,"about_ca_topic_score_gemma":0.00001993293,"domain_scores_codex":[0.9981526,0.0001418739,0.0002480154,0.0009579477,0.000127653,0.0003719551],"domain_scores_gemma":[0.9968813,0.000738364,0.0002919911,0.001348353,0.0006523666,0.00008761899],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0003951039,0.0004133977,0.0006338631,0.00332084,0.0003872303,0.000009088102,0.002796182,0.0166791,0.0006486137,0.9717163,0.001199749,0.001800477],"study_design_scores_gemma":[0.001228843,0.0001084018,0.0001333911,0.0001681819,0.00019232,0.000004769435,0.001415161,0.1354489,0.001913908,0.8568255,0.001996744,0.0005638782],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1282127,0.0001061308,0.8552523,0.0005554725,0.0001229571,0.01239328,0.0001535888,0.0001762997,0.003027192],"genre_scores_gemma":[0.9857352,0.00008663978,0.006275703,0.00003992262,0.0001260416,0.0002090355,0.00007232654,0.00007632018,0.007378836],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8575224,"threshold_uncertainty_score":0.9917834,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1210479625671202,"score_gpt":0.2718438201968935,"score_spread":0.1507958576297734,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}