Cyclic and supercyclic weighted composition operators on the Fock space

Abstract

We study the cyclic and supercyclic dynamical properties of weighted composition operators on the Fock space F 2 . A complete characterization of cyclicity which depends on the derivative of the symbol for the composition operator and zeros of the weight function is provided. It is further shown that the space fails to support supercyclic weighted composition operators. As a consequence, we also noticed that the space supports no cyclic multiplication operator. 1 π e −|z| 2 dA(z) where dA is the Lebesgue measure in the complex plane C. It is a reproducing kernel Hilbert space with inner product f, g = C f (z)g(z)dµ(z), norm f 2 := f, f , and kernel function K w (z) = e z,w .

Dynamics of weighted composition operators on weighted Banach spaces of entire functions

“…The dynamics of composition and weighted composition operators on spaces of holomorphic functions has recently attracted the attention of many researchers. See for instance [5], [6], [7], [11], [16], [21] [22], [27], [31], and the references therein.…”