Sur certaines extensions du théorème d'approximation de Bernstein
type: Item
instance of: scholarly article
title: Sur certaines extensions du théorème d'approximation de Bernstein
zbMATH Open document ID: 0575.41025
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let X be a compact space and A a closed subalgebra of C(X). The real functions in A define closed equivalence classes in X. A theorem of Silov states that a continuous function f is in A if and only if the restriction of f to each equivalence class is in the space of restrictions of elements of A. Bishop obtained an improved version of this result. In the present paper, generalizations of these results of Silov and Bishop are obtained in which firstly A is replaced by a vector subspace E of C(X). In turn E is replaced by a cone of functions with values in a real or complex Banach space.
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 3919002
zbMATH Keywords: Bernstein theorem
zbMATH Keywords: Silov theorem
zbMATH Keywords: Bishop theorem
author: Denis Feyel
author: Arnaud De La Pradelle
reviewed by: H. R. Dowson
MaRDI profile type: Publication
full work available at URL: pjm.1984.115.81
OpenAlex ID: W2027460852
DOI: 10.2140/PJM.1984.115.81
description: scientific article; zbMATH DE number 3919002