Mean ergodicity of multiplication operators in weighted Dirichlet spaces
Abstract
We characterize bounded multiplication operators in weighted Dirichlet spaces that are power bounded, Ces\`aro bounded and uniformly Kreiss. Moreover, we show the equivalence in such spaces between mean ergodicity and Ces\`aro 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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