Nested sequences of balls, uniqueness of Hahn-Banach extensions and the Vlasov property.
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.
(\(w^\ast\)-) asymptotic norming properties
scientific article; zbMATH DE number 2012048
scientific article