## Abstract and Applied Analysis

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

#### 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 $T$ to the operator norm convergence of certain sequences of operators generated by $T$, 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 179027, 16 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.aaa/1395858209

Digital Object Identifier
doi:10.1155/2014/179027

Mathematical Reviews number (MathSciNet)
MR3166576

Zentralblatt MATH identifier
07021878

#### Citation

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

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