Mean ergodicity of multiplication operators in weighted Dirichlet spaces
Complex Variables
2025-03-06 v1 Functional Analysis
Abstract
We characterize bounded multiplication operators in weighted Dirichlet spaces that are power bounded, Ces\`{a}ro bounded and uniformly Kreiss. Moreover, we show the equivalence in such spaces between mean ergodicity and Ces\`{a}ro boundedness for multiplication operators. We perform the same study for adjoints of multiplication operators. As a particular example, we obtain a uniform mean ergodic multiplication operator in Dirichlet spaces that fails to be power bounded.
Keywords
Cite
@article{arxiv.2503.03678,
title = {Mean ergodicity of multiplication operators in weighted Dirichlet spaces},
author = {Antonio Bonilla and Daniel Seco},
journal= {arXiv preprint arXiv:2503.03678},
year = {2025}
}