# HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE'S THEOREM

• Hallack Andre Arbex (Departamento de Matematica Universidade Federal de Juiz de Fora)
• Published : 2007.02.28
• 79 4

#### 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

#### References

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