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This short chapter digs a bit deeper into the finer parts of the spectrum of the Cesàro operator on \(\ell ^2\) . In particular, we compute its essential spectrum, essential norm, and Fredholm index. Some of these ideas will reappear in Chap. 10 when we discuss the Fredholm theory for two related continuous versions of the Cesàro operator.

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Fredholm Theory for the Cesàro Operator

  • 章节

  • 发表日期：

    2026年

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  • Javad Mashreghi,
  • William T. Ross

摘要

This short chapter digs a bit deeper into the finer parts of the spectrum of the Cesàro operator on \(\ell ^2\) . In particular, we compute its essential spectrum, essential norm, and Fredholm index. Some of these ideas will reappear in Chap. 10 when we discuss the Fredholm theory for two related continuous versions of the Cesàro operator.