Extreme points and the diameter norm
type: Item
instance of: scholarly article
title: Extreme points and the diameter norm
zbMATH Open document ID: 1073.46016
published in: Rocky Mountain Journal of Mathematics
publication date: 2005-03-10T00:00:00Z
review text: Let \(X\) be an infinite compact Hausdorff space. Let \(A \subset C(X)\) be a closed, point separating subspace containing constants \(C\) (real scalars). It is well-known that \(A\) can be identified with the space of affine continuous functions on its state space. If one equips the quotient space \(A/C\) with the norm \(\| [f]\| = \text{diam}(f(X))\), the reviewer and \textit{A. K. Roy} [J. Aust. Math. Soc. 70, 323--335 (2001; Zbl 1027.46009)] have given a complete description of the extreme points of the dual unit ball of \(A/C\) under the assumption that every extreme point of the state space is a split face. In this paper, the authors show that the same description holds when \(A\) satisfies the unique decomposition property. When the state space is a Choquet simplex, \(A\) satisfies both the conditions described above.
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 2143229
zbMATH Keywords: extreme points
zbMATH Keywords: spaces of continuous functions
zbMATH Keywords: diameter norm
author: Juan J. Font
author: Manuel Sanchis
reviewed by: T.S.S.R.K. Rao
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069802
OpenAlex ID: W2022987474
cites work: Q3900495
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DOI: 10.1216/RMJM/1181069802
description: scientific article; zbMATH DE number 2143229