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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Sung Guen Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0009854).
A. Peris was supported in part by MICINN and FEDER, Project MTM2010-14909, and by Generalitat Valenciana, Project PROMETEO/2008/101.
Hyun Gwi Song(Corresponding Author) is supported partially by BK21 program.
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Kim, S.G., Peris, A. & Song, H.G. Numerically Hypercyclic Operators. Integr. Equ. Oper. Theory 72, 393–402 (2012). https://doi.org/10.1007/s00020-012-1944-1
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DOI: https://doi.org/10.1007/s00020-012-1944-1