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Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces

Author

Listed:
  • Angela A. Albanese
  • José Bonet
  • Werner J. Ricker

Abstract

Well-known Banach space results (e.g., due to J. Koliha and Y. Katznelson/L. Tzafriri), which relate conditions on the spectrum of a bounded operator to the operator norm convergence of certain sequences of operators generated by , are extended to the class of quojection Fréchet spaces. These results are then applied to establish various mean ergodic theorems for continuous operators acting in such Fréchet spaces and which belong to certain operator ideals, for example, compact, weakly compact, and Montel.

Suggested Citation

  • Angela A. Albanese & José Bonet & Werner J. Ricker, 2014. "Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-16, January.
    • Handle: RePEc:hin:jnlaaa:179027
    DOI: 10.1155/2014/179027
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