Special uniform approximations of continuous vector-valued functions. II: Special approximations in \(C_{X}(T)\otimes C_{Y}(S)\).
type: Item
instance of: scholarly article
title: Special uniform approximations of continuous vector-valued functions. II: Special approximations in \(C_{X}(T)\otimes C_{Y}(S)\).
zbMATH Open document ID: 1052.41020
DOI: 10.1016/S0021-9045(03)00103-5
author: Vlad Timofte
published in: Journal of Approximation Theory
publication date: 2003-08-25T00:00:00Z
review text: Continuing his previous investigations [see J. Approximation Theory 119, No. 2, 291--299 (2002; Zbl 1023.46008)], the author defines and studies a new kind of approximation, called special uniform approximation, for functions in the spaces \(\,C_{X\otimes Y}(T\times S)\,\) and \(\, C_ \infty(T\times S,X\otimes Y)\,\) by elements in the tensor products \(C_ X(T)\otimes C_ Y(S)\,\) and \(C_ 0(T,X)\otimes C_ 0(S,Y),\, \) respectively. Here \(T,S\) are Hausdorff topological spaces and \(X,Y\) Hausdorff locally convex spaces over \(\mathbb R\) or \(\mathbb C\). As corollary he obtains, among other results, the density of \(C_ 0(T,X)\otimes C_ 0(S,Y),\, \) in \(C_ 0(T\times S,X\otimes Y)\) with respect to the inductive limit topology.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 46A32
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 1970541
zbMATH Keywords: tensor products
zbMATH Keywords: uniform approximation
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
cites work: Q3704352
cites work: Q4200714
cites work: Q4150705
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cites work: Special uniform approximations of continuous vector-valued functions. I: Special approximations in \(C_X(T)\)
description: scientific article; zbMATH DE number 1970541