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http://dx.doi.org/10.4134/BKMS.2007.44.1.117

HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE'S THEOREM  

Hallack Andre Arbex (Departamento de Matematica Universidade Federal de Juiz de Fora)
Publication Information
Bulletin of the Korean Mathematical Society / v.44, no.1, 2007 , pp. 117-123 More about this Journal
Abstract
In this paper, we first adapt Runge's Theorem to work on certain domains in any complex Banach space. Then, using this result, we extend Birkhoff's Theorem on the hypercyclicity of translations on $H(\mathbb{C})$ and Costakis' and Sambarino's result on the existence of common hypercyclic functions for uncountable families of translations on $H(\mathbb{C})$ to subs paces of $H_b(E)$ (in some cases all of $H_{b}$(E)), E being in a large class of Banach spaces.
Keywords
hypercyclic operators; hypercyclicity;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 1  (Related Records In Web of Science)
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