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arXiv · 1310.5083

Mean ergodic properties of the continuous Ces\`aro operators

Angela A. Albanese·José Bonet·Werner J. Ricker
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Abstract

Various properties of the (continuous) Ces\`aro operator $\mathsf{C}$, acting on Banach and Fr\'echet spaces of continuous functions and $L^p$-spaces, are investigated. For instance, the spectrum and point spectrum of $\mathsf{C}$ are completely determined and a study of certain dynamics of $\mathsf{C}$ is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of $\mathsf{C}$ acting in the various spaces is identified.

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Angela A. Albanese, José Bonet, Werner J. Ricker. 2013-10-18. Mean ergodic properties of the continuous Ces\`aro operators. https://arxiv.org/abs/1310.5083

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