Uniform convergence and spectra of operators in a class of Fréchet spaces
type: Item
instance of: scholarly article
title: Uniform convergence and spectra of operators in a class of Fréchet spaces
zbMATH Open document ID: 1472.47006
DOI: 10.1155/2014/179027
author: Angela A. Albanese
author: José Bonet
author: Werner J. Ricker
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 7021878
zbMATH Keywords: spectrum
zbMATH Keywords: operator norm convergence
zbMATH Keywords: quojection Fréchet spaces
zbMATH Keywords: mean ergodic theorems
zbMATH Keywords: operator ideals
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/179027
OpenAlex ID: W2021878340
Wikidata QID: Q59035801
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description: scientific article; zbMATH DE number 7021878