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arXiv · 1707.04726

The Cesàro operator in weighted $\ell_1$ spaces

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

Unlike for $\ell_p$, $1<p\leq\infty$, the discrete Cesàro operator $C$ does not map $\ell_1$ into itself. We identify precisely those weights $w$ such that $C$ does map $\ell_1(w)$ continuously into itself. For these weights a complete description of the eigenvalues and the spectrum of $C$ are presented. It is also possible to identify all $w$ such that $C$ is a compact operator in $\ell_1(w)$. The final section investigates the mean ergodic properties of $C$ in $\ell_1(w)$. Many examples are presented in order to supplement the results and to illustrate the phenomena that occur.

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BibTeXRIS

Angela A. Albanese, José Bonet, Werner J. Ricker. 2017-07-15. The Cesàro operator in weighted $\ell_1$ spaces. https://doi.org/10.1002/mana.201600509

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