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

Abstract

For holomorphic pairs of symbols (u,ψ), we study various structures of the weighted composition operator W(u,ψ)f=u⋅f(ψ) defined on the Fock spaces Fp. We have identified operators W(u,ψ) 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(b1−a)|, where a and b are coefficients from linear expansion of the symbol ψ. The spectrum of the operators is also determined and applied further to prove results about uniform mean ergodicity.