Nested sequences of balls, uniqueness of Hahn-Banach extensions and the Vlasov property.
type: Item
instance of: scholarly article
title: Nested sequences of balls, uniqueness of Hahn-Banach extensions and the Vlasov property.
zbMATH Open document ID: 1062.46014
author: Pradipta Bandyopadhyay
author: A. K. Roy
published in: Rocky Mountain Journal of Mathematics
publication date: 2003-12-03T00:00:00Z
full work available at URL: CONT33-1.html
review text: Let \(X\) be a real vector space and let \(p:X\to\mathbb R\) be a sublinear functional. The authors generalize and localize in a natural way some results by \textit{E.~Oja} and the reviewer [Stud. Math. 117, No. 3, 289--306 (1996; Zbl 0854.46014)] by giving, in terms of intersection properties of sequences of nested ``\(p\)-balls'' and subspaces in a quotient space, necessary and sufficient conditions for a functional on a subspace of \(X\) dominated by \(p\) to have a unique extension to \(X\) dominated by \(p\). Several applications and examples are discussed (concerning, e.g., Banach limits, uniqueness of extensions of positive linear functionals, uniqueness in Strassen's theorem). The obtained results are used to characterize \(w^\ast\)-asymptotic norming properties in terms of nested sequences of balls.
reviewed by: Märt Põldvere
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 2012048
zbMATH Keywords: sublinear functionals
zbMATH Keywords: nested sequences of (\(p\)-)balls
zbMATH Keywords: uniqueness of Hahn-Banach extensions
zbMATH Keywords: (\(w^\ast\)-) asymptotic norming properties
zbMATH Keywords: Hahn-Banach smoothness
zbMATH Keywords: Vlasov property
MaRDI profile type: Publication
OpenAlex ID: W2063792150
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DOI: 10.1216/RMJM/1181069986
description: scientific article; zbMATH DE number 2012048