{"id":"W2061032104","doi":"10.1090/s0002-9947-2014-06336-8","title":"Characterization of closed ideals with bounded approximate identities in commutative Banach algebras, complemented subspaces of the group von Neumann algebras and applications","year":2014,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Subalgebra; Idempotence; Von Neumann algebra; Bounded function; Group (periodic table); Ideal (ethics); Pure mathematics; Group algebra; Group ring; Combinatorics; Discrete mathematics; Von Neumann architecture; Algebra over a field","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005909528,0.0001941002,0.0006208986,0.00005800345,0.0002161915,0.00002140295,0.0004744356,0.00004323423,0.00003528027],"category_scores_gemma":[0.00007680912,0.0001210145,0.000188581,0.0009023086,0.0019757,0.0001612468,0.00006116297,0.0002627525,5.652014e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005675522,"about_ca_system_score_gemma":0.0000421896,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001028773,"about_ca_topic_score_gemma":0.0001218816,"domain_scores_codex":[0.9980476,0.0003388531,0.0006499429,0.0002096474,0.0005147544,0.0002391973],"domain_scores_gemma":[0.9976044,0.0008673797,0.0006844674,0.000620269,0.0001743922,0.00004904486],"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":[0.0002528984,0.002575936,0.007140129,0.004641813,0.0009989531,1.955719e-7,0.02322026,0.0001993963,0.2328666,0.7247399,0.00003525679,0.003328587],"study_design_scores_gemma":[0.003110335,0.0007194385,0.04066679,0.000897296,0.0006085353,0.00001782254,0.02610312,0.01925482,0.1184292,0.789482,0.00004697899,0.0006636485],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6880286,0.000006552929,0.310603,0.0002850587,0.000006598948,0.0008967835,0.00006023747,0.00001869432,0.00009445881],"genre_scores_gemma":[0.9790975,0.0000380275,0.02055109,0.00003981364,0.000006717111,0.000180458,0.000006755663,0.00003226838,0.00004730748],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2910689,"threshold_uncertainty_score":0.727955,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01905653010916129,"score_gpt":0.2995104417823879,"score_spread":0.2804539116732266,"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."}}