Mean ergodic composition operators on generalized Fock spaces

Abstract

Every bounded composition operator $$C_{\psi }$$ defined by an analytic symbol $$\psi $$ on the complex plane when acting on generalized Fock spaces $$\mathcal {F}_{\varphi }^{p}, 1 \le p \le \infty $$, and $$p=0$$, is power bounded. Mean ergodic and uniformly mean ergodic bounded composition operators on these spaces are characterized in terms of the symbol. The behaviour for $$p=0$$ and $$p=\infty $$ differs. The set of periodic points of these operators is also determined.