COMPOSITION OPERATORS ON THE FOCK SPACE OF VECTOR-VALUED ANALYTIC FUNCTIONS

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