Year: 2017
Type: preprint
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 $m\in\mathbb{N}$.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Generalitat Valenciana
Awards: G3710865097, G951603189
OpenAlex ID: W2963597183