Measures under the flat norm as ordered normed vector space
type: Item
instance of: scholarly article
title: Measures under the flat norm as ordered normed vector space
zbMATH Open document ID: 1390.28004
author: Piotr Gwiazda
author: Anna Marciniak-Czochra
author: Horst R. Thieme
published in: Positivity
publication date: 2018-04-19T00:00:00Z
review text: The space of all real Borel measures \(\mathcal{M}(S)\) on a metric space \(S\) is usually considered by the variational norm. In this paper the authors consider that space under the \textit{flat norm}; i.e., as a linear subspace of the dual of Lip\((S)\), the space of bounded Lipschitz continuous functions on \(S\) endowed by the usual Lipschitz norm. Such a norm is complete if and only if \(S\) is uniformly discrete (and in such case it is equivalent by the variational norm). Under the flat norm compactness and continuity of semiflows on \(\mathcal{M}(S)_+\) are established under weaker conditions. Completeness and convergence of sequence in \(\mathcal{M}(S)_+\) are also studied.
reviewed by: Daniele Puglisi
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 46E27
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 47J10
Mathematics Subject Classification ID: 58C40
Mathematics Subject Classification ID: 47N60
zbMATH DE Number: 6861654
zbMATH Keywords: measures
zbMATH Keywords: ordered normed vector space
zbMATH Keywords: homogeneous maps
zbMATH Keywords: spectral radius
zbMATH Keywords: Krein-Rutman theorem
zbMATH Keywords: dynamical systems
MaRDI profile type: Publication
full work available at URL: s11117-017-0503-z
OpenAlex ID: W2618843012
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Measures under the flat norm as ordered normed vector space (DOI)
DOI: 10.1007/S11117-017-0503-Z