Resolvent growth condition for the composition operator on the Fock space

Abstract

For each analytic map ψ on the complex plane C, we study the Ritt’s resolvent growth condition for the composition operator Cψ:f→f∘ψ on the Fock space F2. We show that Cψ satisfies such a condition if and only if it is either compact or reduces to the identity operator. As a consequence, it is shown that the Ritt’s resolvent condition and the unconditional Ritt’s condition for Cψ are equivalent.