{"paper":{"title":"Szemeredi's theorem, frequent hypercyclicity and multiple recurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"George Costakis, Ioannis Parissis","submitted_at":"2010-08-24T11:50:07Z","abstract_excerpt":"Let T be a bounded linear operator acting on a complex Banach space X and (\\lambda_n) a sequence of complex numbers. Our main result is that if |\\lambda_n|/|\\lambda_{n+1}| \\to 1 and the sequence (\\lambda_n T^n) is frequently universal then T is topologically multiply recurrent. To achieve such a result one has to carefully apply Szemer\\'edi's theorem in arithmetic progressions. We show that the previous assumption on the sequence (\\lambda_n) is optimal among sequences such that |\\lambda_n|/|\\lambda_{n+1}| converges in [0,+\\infty]. In the case of bilateral weighted shifts and adjoints of multip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4017","kind":"arxiv","version":2},"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"}