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arXiv · 2503.03678

Mean ergodicity of multiplication operators in weighted Dirichlet spaces

Antonio Bonilla·Daniel Seco
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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.

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Antonio Bonilla, Daniel Seco. 2025-03-05. Mean ergodicity of multiplication operators in weighted Dirichlet spaces. https://arxiv.org/abs/2503.03678

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