Hypercyclicity for translations through Runge's Theorem
Bull. Korean Math. Soc. 2007 Vol. 44, No. 1, 117-123 Printed March 1, 2007
Andre Arbex Hallack Universidade Federal de Juiz de Fora
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 subspaces of $H_b(E)$ (in some cases all of $H_b(E)$), $E$ being in a large class of Banach spaces.