Unbounded Chaotic Weighted Pseudo-shift

Abstract

In this paper, based on the work of Vijay K. Srivastava and Harish Chandra, we give a characterization of the unbounded hypercyclic weighted pseudo-shift operator $w{C}_{\phi }$ on ${\ell }^p$ or $c_0$. Moreover we use the hypercyclicity criterion of Bès, Chan, and Seubert to give a necessary and sufficient condition in order that $w{C}_{\phi }$ be a chaotic operator.

20 pages