Uniform mean ergodicity of \(C_0\)-semigroups in a class of Fréchet spaces
type: Item
instance of: scholarly article
title: Uniform mean ergodicity of \(C_0\)-semigroups in a class of Fréchet spaces
zbMATH Open document ID: 1314.47060
author: Angela A. Albanese
author: José Bonet
author: Werner J. Ricker
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2014-09-09T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.facm/1403811847
review text: In this work, the authors present an extensive study of uniform mean ergodicity of \(C_0\)-semigroups of bounded linear operators on quojection Fréchet spaces, i.e., on spaces which are quotients of countable products of Banach spaces. They extend and generalize some characterizations of uniform mean ergodicity from the Banach spaces setting to that of quojection Fréchet spaces and they show that this extension fails to hold for all Fréchet spaces. Moreover, they give many interesting applications of their results for some concrete classes of \(C_0\)-semigroups, in particular, Fréchet function and sequence spaces.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 6341728
zbMATH Keywords: \(C_0\)-semigroup
zbMATH Keywords: uniform mean ergodicity
zbMATH Keywords: quojection and prequojection Fréchet spaces
reviewed by: Antonios Manoussos
MaRDI profile type: Publication
OpenAlex ID: W1560726590
cites work: Q4012524
cites work: Q3398912
cites work: Grothendieck spaces with the Dunford-Pettis property
cites work: On Mean Ergodic Operators
cites work: \(C_{0}\)-semigroups and mean ergodic operators in a class of Fréchet spaces
cites work: Mean ergodic semigroups of operators
cites work: Montel resolvents and uniformly mean ergodic semigroups of linear operators
cites work: Convergence of arithmetic means of operators in Fréchet spaces
cites work: Mean ergodic theorems for bi-continuous semigroups
cites work: Some permanence results of the Dunford-Pettis and Grothendieck properties in lcHs
cites work: Q2716079
cites work: Frechet Spaces with Nuclear Kothe Quotients
cites work: On a problem of Bellenot and Dubinsky
cites work: Q3496758
cites work: Mean ergodic operators and reflexive Fréchet lattices
cites work: Schauder decompositions and the Grothendieck and Dunford--Pettis properties in Köthe echelon spaces of infinite order
cites work: A note on quojections
cites work: A note on strictly regular Fréchet spaces
cites work: Twisted Fréchet spaces of continuous functions
cites work: Q3254057
cites work: Abstract Ergodic Theorems and Weak Almost Periodic Functions
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Q3244654
cites work: Q3918541
cites work: Semi-groups of operators in locally convex spaces
cites work: Semigroups of operators in locally convex spaces
cites work: Ergodic theorems. With a supplement by Antoine Brunel
cites work: On the Uniform Ergodic Theorem
cites work: On the Uniform Ergodic Theorem. II
cites work: Q4164139
cites work: Q4340900
cites work: Q4015695
cites work: Fréchet Spaces without continuous Norms and without Bases
cites work: Strongly nonnorming subspaces and prequojections
cites work: Unbounded linear operators and nuclear Köthe quotients
cites work: Quasi-reflexive Fréchet spaces and mean ergodicity
cites work: Quasi-reflexive Fréchet spaces and contractively power bounded operators
cites work: Q4049667
cites work: On Two Problems of Mityagin
cites work: Q3874718
DOI: 10.7169/FACM/2014.50.2.8
description: scientific article; zbMATH DE number 6341728