Mean ergodicity and spectrum of the Cesàro operator on weighted \(c_0\) spaces

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• 作者：Angela A. Albanese ; José Bonet ; Werner J. Ricker
• 关键词：Cesàro operator ; Weighted \(c_0\) ; space ; Spectrum ; Compact operator ; Mean ergodic operator
• 刊名：Positivity
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：20
• 期：4
• 页码：761-803
• 全文大小：815 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Operator Theory
  Potential Theory
  Calculus of Variations and Optimal Control
  Econometrics
  
• 出版者：Birkh盲user Basel
• ISSN：1572-9281
• 卷排序：20

文摘

A detailed investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator \(\mathsf {C}\) acting on the weighted Banach sequence space \(c_0(w)\) for a bounded, strictly positive weight w. New features arise in the weighted setting (e.g. existence of eigenvalues, compactness, mean ergodicity) which are not present in the classical setting of \(c_0\).