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

The Cesàro operator in weighted $\ell_1$ spaces

Angela A. Albanese
Membro del Collaboration Group
;
2018

Abstract

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

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/425938
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact