A Weierstrass approximation theorem for topological vector spaces
type: Item
instance of: scholarly article
title: A Weierstrass approximation theorem for topological vector spaces
zbMATH Open document ID: 0562.41027
DOI: 10.1016/0021-9045(84)90049-2
author: Vincent J. Bruno
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: \textit{J. B. Prolla} and \textit{S. Machado} [Trans. Am. Math. Soc. 186(1973), 247-258 (1974; Zbl 0289.46024)] proved that if E and F are real locally convex Hausdorff spaces, then the polynomial operators of finite type are dense in C(E,F) equipped with the compact-open topology. In the paper the author proves the analogous results when E and F are not necessarily convex and: 1) E has a sequence of projections with the Grothendieck approximation property [\textit{H. H. Schaeffer}, Topological vector spaces (1972; Zbl 0217.160), pp. 108-115]; 2) F has a sequence with the Grothendieck approximation property.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 3895601
zbMATH Keywords: polynomial operator
zbMATH Keywords: compact-open topology
zbMATH Keywords: Grothendieck approximation property
reviewed by: D. K. Ugulava
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90049-2
OpenAlex ID: W2072468965
cites work: A Weierstrass theorem for real, separable Hilbert spaces
cites work: Weighted Grothendieck Subspaces
cites work: Q5613420
cites work: The Sequence Spaces l (pv ) and m (pv )
Recommended article: Q4010394
Recommended article: Q4444593
Recommended article: Generalization of a Real-Analysis Result to a Class of Topological Vector Spaces
Recommended article: The Oka-Weil theorem in topological vector spaces
Recommended article: The approximate fixed point property in Hausdorff topological vector spaces and applications
Recommended article: A generalization of the Gleason-Kahane-Zelazko theorem to topological vector spaces
Recommended article: The Weierstrass approximation theorem for maps between real algebraic varieties
Recommended article: Leray-Schauder alternatives for approximable maps in topological vector spaces
Recommended article: On the Riesz representation theorem in topological vector spaces
Recommended article: The Mackey- Ulam theorem in topological vector spaces
description: scientific article; zbMATH DE number 3895601