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arXiv · 1704.02251

The Cesàro operator on power series spaces

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

The discrete Cesàro operator $\mathsf{C}$ is investigated in the class of power series spaces $Λ_0(α)$ of finite type. Of main interest is its spectrum, which is distinctly different when the underlying Fréchet space $Λ_0(α)$ is nuclear as for the case when it is not. Actually, the nuclearity of $Λ_0(α)$ is characterized via certain properties of the spectrum of $\mathsf{C}$. Moreover, $\mathsf{C}$ is always power bounded, uniformly mean ergodic and, whenever $Λ_0(α)$ is nuclear, also has the property that the range $(I-\mathsf{C})^m(Λ_0(α))$ is closed in $Λ_0(α)$, for each $m\in\mathbb{N}$.

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Angela A. Albanese, José Bonet, Werner J. Ricker. 2017-04-07. The Cesàro operator on power series spaces. https://arxiv.org/abs/1704.02251

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