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 iden-tified with the sequence space ℓ2(N). We use the the hypercyclic-ity Criterion of Bès, Chan and Seubert and the program of K.-G. Grosse–Erdmann to give a necessary and sufficient condition in or-der that T be a chaotic operator. The chaoticity of differentiation which correspond to the annihilation operator in quantum radia-tion field theory is in view, since the Bargmann space is an infinite dimensional separable complex Hilbert space. 1