Composition Operators on The Fock Space of Vector-Valued Analytic Functions

Abstract

In this note, we study some properties of the composition operator $C_{\phi }$ on the Fock space ${\mathcal{F}}_X^2$ of $X$-valued analytic functions in $\mathbb{C}$. We give a necessary and sufficient condition for a bounded operator on ${\mathcal{F}}_X^2$ to be a composition operator and for the adjoint operator of a composition operator to be also a composition operator on ${\mathcal{F}}_X^2$. We also give characterizations of normal, unitary, and co-isometric composition operators on ${\mathcal{F}}_X^2$.