{"paper":{"title":"The Ces\\`aro operator on power series spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Angela A. Albanese, Jos\\'e Bonet, Werner J. Ricker","submitted_at":"2017-04-07T14:46:54Z","abstract_excerpt":"The discrete Ces\\`aro operator $\\mathsf{C}$ is investigated in the class of power series spaces $\\Lambda_0(\\alpha)$ of finite type. Of main interest is its spectrum, which is distinctly different when the underlying Fr\\'echet space $\\Lambda_0(\\alpha)$ is nuclear as for the case when it is not. Actually, the nuclearity of $\\Lambda_0(\\alpha)$ is characterized via certain properties of the spectrum of $\\mathsf{C}$. Moreover, $\\mathsf{C}$ is always power bounded, uniformly mean ergodic and, whenever $\\Lambda_0(\\alpha)$ is nuclear, also has the property that the range $(I-\\mathsf{C})^m(\\Lambda_0(\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02251","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"}