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The Cesàro operator on smooth sequence spaces of finite type

  • Ersin Kızgut
Original Paper
  • 14 Downloads

Abstract

The discrete Cesàro operator \(\mathsf {C}\) is investigated in the class of smooth sequence spaces \(\lambda _0(A)\) of finite type. This class contains properly the power series spaces of finite type. Of main interest is its spectrum, which is distinctly different in the cases when \(\lambda _0(A)\) is nuclear and when it is not. The nuclearity of \(\lambda _0(A)\) is characterized via certain properties of the spectrum of \(\mathsf {C}\). Moreover, \(\mathsf {C}\) is always power bounded and uniformly mean ergodic on \(\lambda _0(A)\).

Keywords

Cesàro operator Smooth sequence spaces of finite type Generalized power series spaces Spectrum Fréchet space 

Mathematics Subject Classification

47A10 47B37 46A45 46A04 

Notes

Acknowledgements

The author wishes to thank Prof. José Bonet for crucial suggestions and discussions. He is also thankful to the anonymous referees as well as Prof. David Jornet for their careful reviewing.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universitat Politècnica de ValènciaValenciaSpain

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