Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces
Functional Analysis
2021-12-13 v1 Complex Variables
Abstract
Various dynamical properties of the differentiation and Volterra-type integral operators on generalized Fock spaces are studied. We show that the differentiation operator is always supercyclic on these spaces. We further characterize when it is hypercyclic, power bounded and uniformly mean ergodic. We prove that the operator satisfies the Ritt's resolvent condition if and only if it is power bounded and uniformly mean ergodic. Some similar results are obtained for the Volterra-type and Hardy integral operators.
Keywords
Cite
@article{arxiv.2112.05420,
title = {Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces},
author = {José Bonet and Tesfa Mengestie and Mafuz Worku},
journal= {arXiv preprint arXiv:2112.05420},
year = {2021}
}