On Šilov boundary for function spaces
type: Item
instance of: scholarly article
title: On Šilov boundary for function spaces
zbMATH Open document ID: 1356.46020
author: T.S.S.R.K. Rao
author: A. K. Roy
published in: Topology and its Applications
publication date: 2015-08-20T00:00:00Z
review text: This paper is an attempt to generalize classical boundary theory for subspaces of the unital commutative \(C^*\)-algebra \(C(X)\) of continuous complex-valued functions on the compact Hausdorff space \(X\) that contain the unit in \(C(X)\) to those that do not. It owes much to the classic monograph of \textit{R. R. Phelps} entitled `Lectures on Choquet's theorem' [Princeton etc.: Van Nostrand (1966; Zbl 0135.36203); Berlin: Springer (2001; Zbl 0997.46005)] and to his paper [Bull. Am. Math. Soc. 83, 299--312 (1977; Zbl 0382.46005)]. In particular, it is shown that, for closed subspaces \(A\) of \(C(X)\) that separate points in \(X\) but do not contain the unit in \(C(X)\), the closure of the Choquet boundary \(\partial A\) is a `bundle' that coincides with the Šilov boundary `bundle'.
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 46J10
zbMATH DE Number: 6474009
zbMATH Keywords: Shilov boundary
zbMATH Keywords: peak points
zbMATH Keywords: Choquet simplexes
reviewed by: C. M. Edwards
MaRDI profile type: Publication
full work available at URL: j.topol.2015.07.005
OpenAlex ID: W1030270522
cites work: Q5611281
cites work: Subalgebras of \(C^ *\)-algebras
cites work: Subalgebras of C\(^*\)-algebras. II
cites work: On Šilov boundaries for subspaces of continuous functions
cites work: The Shilov boundary of an operator space and the characterization theorems
cites work: Q3329946
cites work: Q4942571
cites work: The Šilov boundary for operator spaces
cites work: A general approach to the notion of Silov boundary
cites work: BANACH ALGEBRAS OF VECTOR-VALUED FUNCTIONS
cites work: The Choquet representation in the complex case
cites work: Q3900496
cites work: Q5508589
cites work: Q4774586
DOI: 10.1016/J.TOPOL.2015.07.005
Recommended article: On Šilov boundaries for subspaces of continuous functions
Recommended article: The Šilov boundary for operator spaces
Recommended article: Shilov boundary for holomorphic functions on some classical Banach spaces
Recommended article: Q3203299
Recommended article: The character spaces and Šilov boundaries of vector-valued Lipschitz function algebras
Recommended article: Notions of boundaries for function spaces
Recommended article: Q3272628
Recommended article: Q3262931
Recommended article: Boundaries for algebras of holomorphic functions on Banach spaces
Recommended article: On a space of Besicovitch functions
description: scientific article; zbMATH DE number 6474009