\(C_{0}\)-continuity of the Fröbenius-Perron semigroup
type: Item
instance of: scholarly article
title: \(C_{0}\)-continuity of the Fröbenius-Perron semigroup
zbMATH Open document ID: 1016.37002
DOI: 10.1155/S0161171202013364
author: Andrés Navas
author: S. Plaza
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50156
full work available at URL: S0161171202013364.html
review text: Summary: We consider the Fröbenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space \(X\) endowed with a finite or a \(\sigma\)-finite regular measure. We prove that if there exists a faithful invariant measure for the semidynamical system, then the Fröbenius-Perron semigroup of linear operators is \(C_{0}\)-continuous in the space \(L_\mu^1(X)\). We also give a geometrical condition which ensures \(C_{0}\)-continuity of the Fröbenius-Perron semigroup of linear operators in the space \(L_\mu^p(X)\) for \(1\leq p<\infty\), as well as in the space \(L_{\text{loc}}^1\).
Mathematics Subject Classification ID: 37A10
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47D60
Mathematics Subject Classification ID: 28D10
zbMATH DE Number: 1780426
zbMATH Keywords: Fröbenius-Perron semigroup
zbMATH Keywords: linear operators
zbMATH Keywords: semidynamical system
zbMATH Keywords: invariant measure
zbMATH Keywords: \(C_0\)-continuity
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description: scientific article; zbMATH DE number 1780426