Three characterizations of polyhedral Banach spaces
type: Item
instance of: scholarly article
title: Three characterizations of polyhedral Banach spaces
zbMATH Open document ID: 0728.46018
DOI: 10.1007/BF01056615
published in: Ukrainian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: An infinite-dimensional Banach space E is called polyhedral, if intersections of all finite dimensional spaces with the unit ball are polyhedra. Three characterizations, up to isomorphism, of such spaces are given. A ``local'' characterization uses a normed set in the unit dual sphere. A ``global'' characterization uses special coverings of the underlying Banach space [cf., \textit{V. Klee}, Stud. Sci. Math. Hung., 21, 415-427 (1986; Zbl 0577.52007)]. An ``internal'' characterization uses covering of the unit ball U(E) by a sequence of vanishing slices \(\{x\in U(E):f_ n(x)\geq 1-\alpha_ n\}\), \(\alpha_ n\to 0\), where \(f_ n\) are norm-1 functionals.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46B07
zbMATH DE Number: 4203056
author: V. P. Fonf
reviewed by: Jerzy Szulga
MaRDI profile type: Publication
cites work: Polyhedral sections of convex bodies
cites work: Variational principle for equations integrable by the inverse problem method
cites work: Polyhedral Banach spaces
cites work: Q3946620
cites work: Massiveness of the set of extreme points of the unit ball in some dual banach spaces
cites work: Q3697821
full work available at URL: https://doi.org/10.1007/bf01056615
OpenAlex ID: W1977602519
description: scientific article; zbMATH DE number 4203056