{"paper":{"title":"A Katznelson-Tzafriri type theorem for Ces\\`aro bounded operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Luciano Abadias","submitted_at":"2015-06-22T14:02:58Z","abstract_excerpt":"We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\\`aro bounded operators of any order $\\alpha>0.$ For this purpose, we use a functional calculus between a new class of fractional Wiener algebras and the algebra of bounded linear operators, whose existence is characterized by the Ces\\`aro boundedness. Finally, we apply the main theorem to get ergodicity results for the Ces\\`aro means of bounded operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06609","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}