This is an announcement for the paper “The Cesàro operator on smooth sequence spaces of finite type” by Ersin Kızguthttps://arxiv.org/search/math?searchtype=author&query=K%C4%B1zgut%2C+E.
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 $λ_0(A)$.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1811.08493