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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Main Authors: Angela A. Albanese, José Bonet, Werner J. Ricker
Format: Article
Language:English
Published: Wiley 2014-01-01
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.
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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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AT josebonet uniformconvergenceandspectraofoperatorsinaclassoffrechetspaces
AT wernerjricker uniformconvergenceandspectraofoperatorsinaclassoffrechetspaces