Reduction of a mean ergodic Markov semigroup on \(C(X)\) into its irreducible components
type: Item
instance of: scholarly article
title: Reduction of a mean ergodic Markov semigroup on \(C(X)\) into its irreducible components
zbMATH Open document ID: 0768.47020
DOI: 10.1007/BF03025763
author: Shizuo Miyajima
published in: Semigroup Forum
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/135185
review text: Let \(T=(T(t))_{t\geq 0}\) be an ergodic \(C_ 0\)-semigroup of Markov operators on \(C(K)\), where \(K\) is compact. The author shows that there exists a mutually disjoint family \((S_ \lambda)_{\lambda\in\Lambda}\) of closed subsets of \(K\) such that \(T\) naturally induces irreducible Markov-semigroups on \(C(S_ \lambda)\). If \(T\) is uniformly ergodic then the peripheral spectrum of the generator \(A\) of \(T\) is determined by that of the components. The results are analogous to those of Niiro-Sawashima in the discrete case. Their proofs depend on Greiner's Perron-Frobenius theory [see \textit{R. Nagel} (ed.), One parameter semigroups of positive operators. Lect. Notes Math. 1184 (1986; Zbl 0585.47030)].
reviewed by: Wolfgang Arendt
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 47A35
zbMATH DE Number: 64385
zbMATH Keywords: Perron-Frobenius theory
zbMATH Keywords: ergodic \(C_ 0\)-semigroup of Markov operators
zbMATH Keywords: irreducible Markov-semigroups
zbMATH Keywords: peripheral spectrum of the generator
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 64385