Spectrums and Uniform Mean Ergodicity of Weighted Composition Operators on Fock Spaces

Werkaferahu Seyoum,Tesfa Mengestie

doi:10.1007/s40840-021-01203-x

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 is also determined and applied further to prove results about uniform mean ergodicity.

Highlights

We denote by H(C) the space of analytic functions on the complex plane C
Weighted composition operators have been a subject of intense studies in the last several years partly because they found applications in the description of isometries on spaces of analytic functions; see the monographs [10,11] for detailed accounts
(i) W(u,ψ) is power bounded on Fp; (ii)n is a bounded sequence; (iii)

Summary

Introduction

We denote by H(C) the space of analytic functions on the complex plane C. For pairs of functions (u, ψ) in H(C), the weighted composition operator W(u,ψ) is defined by W(u,ψ) f = u · f (ψ), f ∈ H(C). The operator generalizes both the composition Cψ

B Tesfa Mengestie

The Multiplication Operator