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For each analytic map $$\psi$$ on the complex plane $$\mathbb {C}$$, we study the Ritt’s resolvent growth condition for the composition operator $$C_{\psi} :f \rightarrow f\circ \psi$$ on the Fock space $${\mathcal {F}}_2$$. We show that $$C_{\psi}$$ 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 $$C_{\psi}$$ are equivalent.

Resolvent growth condition for composition operators on the Fock space