{"id":"W1605783150","doi":"10.4153/cmb-2010-053-5","title":"Injective Convolution Operators on ℓ<sup>∞</sup>(Γ) are Surjective","year":2010,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba; University of Saskatchewan","funders":"","keywords":"Surjective function; Injective function; Invertible matrix; Convolution (computer science); Simple (philosophy); Operator (biology); Algebra over a field; Convolution power","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008441962,0.0005514478,0.0004126212,0.001279175,0.000863324,0.002030974,0.0004918827,0.0003892979,0.00414299],"category_scores_gemma":[0.002409426,0.0003499967,0.0006630187,0.0006383312,0.003097542,0.002232836,0.002057035,0.001247758,0.0004108803],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008140684,"about_ca_system_score_gemma":0.0005552883,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009771005,"about_ca_topic_score_gemma":0.0006456489,"domain_scores_codex":[0.9991515,0.0001551333,0.0000512523,0.0001422995,0.0003091251,0.0001907453],"domain_scores_gemma":[0.9979103,0.0006863872,0.0003494364,0.000198351,0.0004725684,0.0003830605],"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":[0.00006001862,0.00003706615,0.001103087,0.00005666031,0.00001984017,0.0003053129,0.0006237156,0.001259209,0.005852179,0.9785358,0.0004443312,0.01170277],"study_design_scores_gemma":[0.00001627973,0.0000892017,0.00279568,0.000028817,0.00002535739,0.0006327024,0.0004540453,0.01309458,0.008398284,0.9684176,0.006015232,0.00003202346],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7879581,0.0006210319,0.1414931,0.0005431378,0.0001408792,0.00003807156,0.000126984,0.0002296534,0.06884891],"genre_scores_gemma":[0.983812,0.0003195479,0.0075877,0.00009846679,0.0001052043,0.00002916002,0.00006852347,0.00003864998,0.007940712],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00414299,"threshold_uncertainty_score":0.01385969,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01892618615324499,"score_gpt":0.2520740356493084,"score_spread":0.2331478494960634,"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."}}