{"paper":{"title":"Growth orders and ergodicity for absolutely Ces\\`aro bounded operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio Bonilla, Luciano Abadias","submitted_at":"2017-10-09T08:09:56Z","abstract_excerpt":"In this paper, we extend the concept of absolutely Ces\\`aro boundedness to the fractional case. We construct a weighted shift operator belonging to this class of operators, and we prove that if $T$ is an absolutely Ces\\`{a}ro bounded operator of order $\\alpha$ with $0<\\alpha\\le 1,$ then $\\| T^n\\|=o(n^{\\alpha})$, generalizing the result obtained for $\\alpha =1$. Moreover, if $\\alpha > 1$, then $\\|T^{n}\\|= O(n)$. We apply such results to get stability properties for the Ces\\`aro means of bounded operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02981","kind":"arxiv","version":1},"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"}