Spectrums and uniform mean ergodicity of weighted composition operators on Fock spaces

Abstract

For holomorphic pairs of symbols $(u,\psi )$, we study various structures of the weighted composition operator $W_{(u,\psi )}f=u\cdot f(\psi )$ defined on the Fock spaces ${\mathcal{F}}_p$. We have identified operators $W_{(u,\psi )}$ that have power bounded and uniformly mean ergodic properties on the spaces. These properties are described in terms of easy to apply conditions relying on the values $|u(0)|$ and $|u(\frac{b}{1-a})|$ where $a$ and $b$ are coefficients from linear expansion of the symbol $\psi$. The spectrum of the operators are also determined and applied further to prove results about uniform mean ergodicity.

Cited by in corpus (1)

• Supercyclicity and resolvent condition for weighted composition operators