Numerically Hypercyclic Operators |
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| Authors: | Sung?Guen?Kim Alfredo?Peris Email author" target="_blank">Hyun?Gwi?SongEmail author |
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| Institution: | 1.Department of Mathematics,Kyungpook National University,Daegu,Republic of Korea;2.Departament de Matemàtica Aplicada,IUMPA, Universitat Politècnica de València,València,Spain |
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| Abstract: | An operator T acting on a normed space E is numerically hypercyclic if, for some \({(x, x^*)\in \Pi(E)}\), the numerical orbit \({\{x^*(T^n(x)):n\geq 0\}}\) is dense in \({\mathbb{C}}\). We prove that finite dimensional Banach spaces with dimension at least two support numerically hypercyclic operators. We also characterize the numerically hypercyclic weighted shifts on classical sequence spaces. |
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