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Positivity

, Volume 19, Issue 3, pp 659–679 | Cite as

On the continuous Cesàro operator in certain function spaces

  • Angela A. AlbaneseEmail author
  • José Bonet
  • Werner J. Ricker
Article

Abstract

Various properties of the (continuous) Cesàro operator \(\mathsf {C}\), acting on Banach and Fréchet spaces of continuous functions and \(L^p\)-spaces, are investigated. For instance, the spectrum and point spectrum of \(\mathsf {C}\) are completely determined and a study of certain dynamics of \(\mathsf {C}\) is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of \(\mathsf {C}\) acting in the various spaces is identified.

Keywords

Cesàro operator Continuous function spaces \(L^p\)-spaces (Uniformly) mean ergodic operator Hypercyclic operator Supercyclic operator 

Mathematics Subject Classification

Primary 47A10 47A16 47A35 Secondary 46A04 47B34 47B38 

Notes

Acknowledgments

The research of the first two authors was partially supported by the projects MTM2010-15200 and GVA Prometeo II/2013/013 (Spain). The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Angela A. Albanese
    • 1
    Email author
  • José Bonet
    • 2
  • Werner J. Ricker
    • 3
  1. 1.Dipartimento di Matematica e Fisica “E. De Giorgi”Università del SalentoLecceItaly
  2. 2.Instituto Universitario de Matemática Pura y Aplicada IUMPAUniversitat Politécnica de ValénciaValenciaSpain
  3. 3.Math.-Geogr. FakultätKatholische Universität Eichstätt-IngolstadtEichstättGermany

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