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Collectanea Mathematica

, Volume 69, Issue 2, pp 263–281 | Cite as

The Cesàro operator on Korenblum type spaces of analytic functions

  • Angela A. Albanese
  • José Bonet
  • Werner J. Ricker
Article
  • 105 Downloads

Abstract

The spectrum of the Cesàro operator \(\mathsf {C}\), which is always continuous (but never compact) when acting on the classical Korenblum space and other related weighted Fréchet or (LB) spaces of analytic functions on the open unit disc, is completely determined. It turns out that such spaces are always Schwartz but, with the exception of the Korenblum space, never nuclear. Some consequences concerning the mean ergodicity of \(\mathsf {C}\) are deduced.

Keywords

Cesàro operator Weighted spaces of analytic functions Spectrum Fréchet spaces (LB)-spaces Mean ergodicity 

Mathematics Subject Classification

Primary 47A10 47B38 Secondary 46A11 46E10 47A35 47B10 

Notes

Acknowledgements

The research of the first two authors was partially supported by the projects MTM2013-43540-P and MTM2016-76647-P. The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.

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Copyright information

© Universitat de Barcelona 2017

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Fisica “E. De Giorgi”Università del SalentoLecceItaly
  2. 2.Instituto Universitario de Matemática Pura y Aplicada (IUMPA)Universitat Politècnica de ValènciaValenciaSpain
  3. 3.Math.-Geogr. FakultätKatholische Universität Eichstätt-IngolstadtEichstättGermany

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