Abstract
In this article, we investigate the mean ergodicity of composition operators acting on the Hardy space \(H^p({\mathbb {D}})\), \(1\le p<\infty \). Specifically, a composition operator \(C_\varphi \) acting on \(H^p({\mathbb {D}})\) is mean ergodic if and only if \(\varphi \) has an interior fixed point, in which case \(C_\varphi \) is uniformly mean ergodic if and only if \(\varphi \) is an elliptic automorphism of finite order or a non-automorphism that is not inner.
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Acknowledgements
The authors would like to thank the referee for helpful comments and suggestions which improved the presentation of this paper. This work was supported in part by the National Natural Science Foundation of China (Grant Nos 11771323 and 11371276).
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Communicating Editor: Gadadhar Misra
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Han, SA., Zhou, ZH. Mean ergodicity of composition operators on Hardy space. Proc Math Sci 129, 45 (2019). https://doi.org/10.1007/s12044-019-0476-x
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DOI: https://doi.org/10.1007/s12044-019-0476-x