{"id":"W2145513428","doi":"10.1007/s11856-012-0128-7","title":"On typical properties of Hilbert space operators","year":2012,"lang":"en","type":"article","venue":"Israel Journal of Mathematics","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Hungarian Scientific Research Fund; National Science Foundation","keywords":"Mathematics; Hilbert space; Compact operator on Hilbert space; Operator theory; Separable space; Operator norm; Pure mathematics; Nuclear operator; Bounded function; Unitary state; Equivalence (formal languages); Spectral theory; Linear operators; Approximation property; Banach space; Compact operator; Mathematical analysis","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":[0.001502808,0.0002009034,0.00059581,0.0001313103,0.00005394714,0.00001981907,0.0003232131,0.0001272447,0.000114065],"category_scores_gemma":[0.001513137,0.000127696,0.0001905773,0.000127347,0.0001329277,0.0001628218,0.00005372503,0.0003326874,0.00005983266],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005180484,"about_ca_system_score_gemma":0.00008042187,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000011967,"about_ca_topic_score_gemma":7.507944e-7,"domain_scores_codex":[0.9981226,0.0001246112,0.000855056,0.00007330131,0.0005364127,0.0002879975],"domain_scores_gemma":[0.9982032,0.00044835,0.0005628745,0.000316142,0.000276467,0.0001930369],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.0001819381,0.002206098,0.0007564403,0.0005230057,0.0002632632,0.0000174186,0.008002899,0.00001215462,0.01298485,0.9708951,0.003801659,0.0003551691],"study_design_scores_gemma":[0.005446177,0.002520961,0.0004594707,0.005660191,0.001209308,0.002551882,0.03148855,0.0004934107,0.5711063,0.3718542,0.005567844,0.001641744],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9941472,0.0005482159,0.00214834,0.0002051373,0.0003226913,0.0001407482,0.000003234254,0.00001546045,0.002469014],"genre_scores_gemma":[0.9795752,0.00002912031,0.01957437,0.0001129762,0.0002352851,0.00000202762,1.381526e-7,0.00004289632,0.0004280518],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5990409,"threshold_uncertainty_score":0.5207293,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0602861269525102,"score_gpt":0.2939667574055006,"score_spread":0.2336806304529904,"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."}}