{"paper":{"title":"Remarks on common hypercyclic vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2012-09-06T08:10:13Z","abstract_excerpt":"We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator $T$ on a complex Fr\\'echet space $X$ and a set $\\Lambda\\subseteq \\R_+\\times\\C$ which is not of zero three-dimensional Lebesgue measure, the family $\\{aT+bI:(a,b)\\in\\Lambda\\}$ has no common hypercyclic vectors. This allows to answer negatively questions raised by Godefroy and Shapiro and by Aron. We also prove a sufficient condition for a family of scalar multiples of a given operator on a complex Fr\\'echet space to have a common hyper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1213","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"}