Uniform Convergence and Spectra of Operators ina 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 T to the operator norm convergence of certain sequences of operators generated by T, are extended to the class of quojection Fr¿echet spaces.These results are then applied to establish various mean ergodic theorems for continuous operators acting in such Fr¿echet spaces and which belong to certain operator ideals, for example, compact, weakly compact, and Montel.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.Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2014). Uniform Convergence and Spectra of Operators ina Class of Fréchet Spaces. Abstract and Applied Analysis. 2014:1-16. doi:10.1155/2014/179027S116201