{"paper":{"title":"Simultaneous generic approximation by the iterates of the Cesaro operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Theodosios Douvropoulos","submitted_at":"2012-11-05T08:05:58Z","abstract_excerpt":"We show that for the generic sequence (a) of elements in a subset A of a separable locally convex metrisable space V, the sequences [T^k(a)]_n, n=1,2,... are dense in the convex hull convA of A for all k=1,2,...; where T is the Cesaro operator. Further, if convA is dense in V, then for every sequence x_k of elements of V, k=1,2,... there exists a sequence of indices l_n, n=1,2,..., such that, we have the simultaneous approximation that [T^k(a)]_(l_n) converges to x_k as n tends to infinity for all k=1,2,... These phenomena are topologically generic and in the case where A is a vector space the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0783","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"}