HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE'S THEOREM

Title & Authors
HYPERCYCLICITY FOR TRANSLATIONS THROUGH RUNGE'S THEOREM
Hallack Andre Arbex;

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 $\small{H(\mathbb{C})}$ and Costakis' and Sambarino's result on the existence of common hypercyclic functions for uncountable families of translations on $\small{H(\mathbb{C})}$ to subs paces of $\small{H_b(E)}$ (in some cases all of $\small{H_{b}}$(E)), E being in a large class of Banach spaces.
Keywords
hypercyclic operators;hypercyclicity;
Language
English
Cited by
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