Chaotic weighted shifts in Bargmann space

Abstract

This paper deals with the unilateral backward shift operator T on a Bargmann space F ( C ) . This space can be identified with the sequence space ℓ 2 ( N ) . We use the hypercyclicity criterion of Bès, Chan, and Seubert and the program of K.-G. Grosse-Erdmann to give a necessary and sufficient condition in order that T be a chaotic operator. The chaoticity of differentiation which correspond to the annihilation operator in quantum radiation field theory is in view, since the Bargmann space is an infinite-dimensional separable complex Hilbert space.