{"id":"W2076668527","doi":"10.1090/s0002-9939-2013-11709-0","title":"A remark on invariant subspaces of positive operators","year":2013,"lang":"fi","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Linear subspace; Invariant (physics); Reflexive operator algebra; Mathematics; Pure mathematics; Algebra over a field; Computer science; Mathematical physics; Programming language","routes":{"ca_aff":true,"ca_fund":false,"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":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.001322565,0.0005560384,0.001570966,0.00005092833,0.0002431442,0.0001079932,0.001178746,0.0002078302,0.000630624],"category_scores_gemma":[0.001682813,0.0003519127,0.0009522067,0.0009707841,0.00284517,0.0002439106,0.000547519,0.0006710113,0.0001688958],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001470862,"about_ca_system_score_gemma":0.0001225283,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001032537,"about_ca_topic_score_gemma":4.938913e-7,"domain_scores_codex":[0.996599,0.0000854475,0.001174856,0.0005106983,0.0009846286,0.000645342],"domain_scores_gemma":[0.9955412,0.001171545,0.001702139,0.0004731184,0.0008596625,0.0002522979],"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":[0.0001788458,0.0025549,0.002268099,0.003847613,0.001436967,0.000001044176,0.03527362,0.000002858163,0.07575063,0.8455481,0.03214464,0.0009926999],"study_design_scores_gemma":[0.001920767,0.002681521,0.007729336,0.007034922,0.001480879,0.00006279772,0.102528,0.004859835,0.2472441,0.6225182,0.000182409,0.001757195],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9718638,0.00006533143,0.0001188659,0.003589742,0.00006820948,0.001412059,0.00005849928,0.00004784668,0.02277561],"genre_scores_gemma":[0.9812275,0.0001125514,0.01611429,0.000928165,0.0001032401,0.0000798061,7.922981e-7,0.00009636574,0.001337262],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2230298,"threshold_uncertainty_score":0.9998933,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01399999401280856,"score_gpt":0.2521681512798934,"score_spread":0.2381681572670849,"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."}}