{"paper":{"title":"Ces\\`aro bounded operators in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alfredo Peris, Antonio Bonilla, Teresa Berm\\'udez, Vladimir M\\\"uller","submitted_at":"2017-06-12T13:50:00Z","abstract_excerpt":"We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Ces\\`aro bounded and strong Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing absolutely Ces\\`aro bounded operators on $\\ell^p(\\mathbb{N})$, $1\\le p < \\infty$, which are not power bounded, and provide examples of uniformly Kreiss bounded operators which are not absolutely Ces\\`aro bounded. These results complement very limited number of known examples (see \\cite{Shi} and \\cite{AS}). "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03638","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"}