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 T to the operator norm convergence of certain sequences of operators generated by T, are extended to the class of quojection Fréchet spaces. These re...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/179027 |
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| author | Angela A. Albanese José Bonet Werner J. Ricker |
| author_facet | Angela A. Albanese José Bonet Werner J. Ricker |
| author_sort | Angela A. Albanese |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9cd1d6dd74a84809a68a6a2691403e62 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9cd1d6dd74a84809a68a6a2691403e622025-08-20T02:20:18ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/179027179027Uniform Convergence and Spectra of Operators in a Class of Fréchet SpacesAngela A. Albanese0José Bonet1Werner J. Ricker2Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, C.P.193, 73100 Lecce, ItalyInstituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, 46071 Valencia, SpainMath.-Geogr. Fakultät, Katholische Universität Eichstätt-Ingolstadt, 85072 Eichstätt, GermanyWell-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.http://dx.doi.org/10.1155/2014/179027 |
| spellingShingle | Angela A. Albanese José Bonet Werner J. Ricker Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces Abstract and Applied Analysis |
| title | Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces |
| title_full | Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces |
| title_fullStr | Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces |
| title_full_unstemmed | Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces |
| title_short | Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces |
| title_sort | uniform convergence and spectra of operators in a class of frechet spaces |
| url | http://dx.doi.org/10.1155/2014/179027 |
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