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arXiv · 1811.08493

The Cesàro operator on smooth sequence spaces of finite type

Ersin Kızgut
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Abstract

The discrete Cesàro operator $\mathsf{C}$ is investigated in the class of smooth sequence spaces $λ_0(A)$ of finite type. This class contains properly the power series spaces of finite type. Of main interest is its spectrum, which is distinctly different in the cases when $λ_0(A)$ is nuclear and when it is not. The nuclearity of $λ_0(A)$ is characterized via certain properties of the spectrum of $\mathsf{C}$. Moreover, $\mathsf{C}$ is always power bounded and uniformly mean ergodic on $λ_0(A)$.

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BibTeXRIS

Ersin Kızgut. 2018-11-20. The Cesàro operator on smooth sequence spaces of finite type. https://doi.org/10.1007/s13398-018-0578-9

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