Dual representations of convex bodies and their polars
type: Item
instance of: scholarly article
title: Dual representations of convex bodies and their polars
zbMATH Open document ID: 0880.52001
DOI: 10.1007/BF02509509
publication date: 1997-06-25T00:00:00Z
review text: The author proves the following Krein-Milman type theorem [see e.g. \textit{K. Leichtweiss}, ``Konvexe Mengen'', Berlin: Dt. Verlag der Wissenschaften (1980; Zbl 0427.52001)]: For a convex body \(C\) in a real Hausdorff locally convex space with \(0\in \text{ int }C\) the following representations are equivalent: \[ C= \bigcap_{x\in\Gamma(C)} H(x) \quad \text{and} \quad C^0 =\text{clco} \exp C^0, \] where \(H(x)\) denotes the supporting half-space in the tangency point \(x\in \Gamma (C)\), \(\exp C^0\) denotes the set of (weakly*) exposed points of the polar \(C^0\) of \(C\), and clco denotes the (weakly*) closed convex hull.
Mathematics Subject Classification ID: 52A05
zbMATH DE Number: 1023827
zbMATH Keywords: convex bodies
zbMATH Keywords: polar bodies
author: Vladimir L. Levin
reviewed by: Eike Hertel
MaRDI profile type: Publication
cites work: Sur certains espaces vectoriels topologiques
cites work: Convex functions, monotone operators and differentiability
full work available at URL: https://doi.org/10.1007/bf02509509
OpenAlex ID: W2067049316
published in: Functional Analysis and Its Applications
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description: scientific article; zbMATH DE number 1023827