Approximation by DC functions and application to representation of a normed semigroup
type: Item
instance of: scholarly article
zbMATH Open document ID: 1315.46050
author: Lixin Cheng
author: Yu Zhou
publication date: 2014-10-10T00:00:00Z
full work available at URL: jca21034.htm
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 6353703
zbMATH Keywords: approximation
zbMATH Keywords: Lipschitz function
zbMATH Keywords: DC function
zbMATH Keywords: representation
zbMATH Keywords: normed semigroup
MaRDI profile type: Publication
title: Approximation by DC functions and application to representation of a normed semigroup
published in: Journal of Convex Analysis
review text: The present article presents an approximation result in the spirit of \textit{M. Cepedello Boiso} [Isr. J. Math. 106, 269--284 (1998; Zbl 0920.46010)], namely, that each continuous function defined on a compact subset \(\Omega \) of a locally convex space \(L\) can be approximated by DC functions. Indeed, the subspace of the so-called DAPS-functions (difference of affine polyhedral support functions) is a lattice in \(C(\Omega )\) and the Kakutani-Krein approximation theorem applies. It is finally stated that, in the case when \(\Omega \) is the \(w^{\ast }\)-compact set \(B_{X^{\ast }}\) of the locally convex space \((X^*,w^{\ast })\), where \(X\) is a Banach space, then \(C(\Omega )^{\ast}\) is the dual of the normed semigroup \(b(X)\) generated by the closed balls in \(X\).
reviewed by: A. Daniilidis
description: scientific article; zbMATH DE number 6353703