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

Abstract

In this note, we study some properties of the composition operator \(C_\varphi\) 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 \(\mathcal{F}_X^2\).