Mean ergodic theorems on norming dual pairs
type: Item
instance of: scholarly article
title: Mean ergodic theorems on norming dual pairs
zbMATH Open document ID: 1301.47014
author: Moritz Gerlach
author: Markus Kunze
published in: Ergodic Theory and Dynamical Systems
publication date: 2014-10-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/1206.5703
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 6359410
zbMATH Keywords: Markovian semigroups
zbMATH Keywords: ergodic theorems
zbMATH Keywords: Cesáro convergence
MaRDI profile type: Publication
OpenAlex ID: W3106162698
arXiv ID: 1206.5703
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DOI: 10.1017/ETDS.2012.187
review text: In the present paper, the classical mean ergodic theorem is extended to the setting of norming dual pairs. In Section~2, the authors give basic definitions and discuss results about norming dual pairs \((X,Y, \langle \cdot, \cdot \rangle)\), where \(X,Y\) are Banach spaces and \(\langle \cdot, \cdot \rangle\) is a duality between \(X\) and \(Y\). In Section~3, they introduce the notion of an ``average scheme'', which are further analyzed in Section~4. In Section 5, the authors consider the convergence of average schemes on \((C_b (E), \mathcal{M} (E))\) under additional assumptions. In Section~6, they provide some counterexamples.
reviewed by: Victor Sharapov
description: scientific article; zbMATH DE number 6359410