The Ces\`aro operator on power series spaces
Angela A. Albanese, Jos\'e Bonet, Werner J. Ricker

TL;DR
This paper studies the spectral properties of the Cesàro operator on power series spaces, revealing how nuclearity influences its spectrum and ergodic behavior, with implications for the structure of these spaces.
Contribution
It characterizes the spectrum of the Cesàro operator on power series spaces and links nuclearity to spectral and ergodic properties, providing new insights into these functional spaces.
Findings
Spectrum varies with nuclearity of the space
Cesàro operator is always power bounded and mean ergodic
Nuclearity implies closedness of certain operator ranges
Abstract
The discrete Ces\`aro operator is investigated in the class of power series spaces of finite type. Of main interest is its spectrum, which is distinctly different when the underlying Fr\'echet space is nuclear as for the case when it is not. Actually, the nuclearity of is characterized via certain properties of the spectrum of . Moreover, is always power bounded, uniformly mean ergodic and, whenever is nuclear, also has the property that the range is closed in , for each .
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Approximation Theory and Sequence Spaces
