{"paper":{"title":"On numerically hypercyclic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2013-02-11T14:16:06Z","abstract_excerpt":"According to Kim, Peris and Song, a continuous linear operator $T$ on a complex Banach space $X$ is called {\\it numerically hypercyclic} if the numerical orbit $\\{f(T^nx):n\\in\\N\\}$ is dense in $\\C$ for some $x\\in X$ and $f\\in X^*$ satisfying $\\|x\\|=\\|f\\|=f(x)=1$. They have characterized numerically hypercyclic weighted shifts and provided an example of a numerically hypercyclic operator on $\\C^2$.\n  We answer two questions of Kim, Peris and Song. Namely, we construct a numerically hypercyclic operator, whose square is not numerically hypercyclic as well as an operator which is not numerically "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2483","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"}