{"id":"W2066703940","doi":"10.1016/j.laa.2007.11.007","title":"Symbolic calculus of operators with unit numerical radius","year":2008,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Numerical range; Mathematics; Bounded function; Hilbert space; Polynomial; Operator norm; Norm (philosophy); Bounded operator; Unit sphere; Operator (biology); RADIUS; Combinatorics; Discrete mathematics; Pure mathematics; Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.00007920738,0.0001173104,0.0002215552,0.00004261997,0.0001941077,0.000005841939,0.0001210371,0.00006575573,0.00009422861],"category_scores_gemma":[0.0000326234,0.00008739108,0.00002889558,0.0002800594,0.0001316078,0.00005113468,0.00003125987,0.0001172115,0.00004629309],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006171058,"about_ca_system_score_gemma":0.00006229225,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008221728,"about_ca_topic_score_gemma":0.00000150976,"domain_scores_codex":[0.9993135,0.00003289943,0.0002097309,0.0001773,0.000123707,0.0001429137],"domain_scores_gemma":[0.9993578,0.0001161117,0.00005742073,0.0002507182,0.000100364,0.0001176268],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0000216615,0.0002449821,0.001047498,0.00005495387,0.00005914531,0.000006450145,0.001064427,0.000008011625,0.00120905,0.9952213,0.0004080884,0.0006543936],"study_design_scores_gemma":[0.01797993,0.003405964,0.02332478,0.0005931535,0.001893294,0.004085362,0.007338805,0.04474542,0.289142,0.1181204,0.4826261,0.006744881],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9720552,0.0003487435,0.02418365,0.0001776106,0.00001137628,0.0004557975,0.0000362137,0.00007294578,0.002658451],"genre_scores_gemma":[0.995762,0.0001034785,0.003014853,0.0001113946,0.00007333712,0.0001016786,0.00001013375,0.00002419938,0.0007989447],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8771009,"threshold_uncertainty_score":0.3563705,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03691766636144843,"score_gpt":0.2845675725917794,"score_spread":0.247649906230331,"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."}}