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Mean ergodicity of multiplication operators in weighted Dirichlet spaces (2503.03678v1)
Published 5 Mar 2025 in math.CV and math.FA
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.