Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 179027, 16 pages.
Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces
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.
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 179027, 16 pages.
First available in Project Euclid: 26 March 2014
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Albanese, Angela A.; Bonet, José; Ricker, Werner J. Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 179027, 16 pages. doi:10.1155/2014/179027. https://projecteuclid.org/euclid.aaa/1395858209