On the relation between linear n-widths and approximation numbers
type: Item
instance of: scholarly article
title: On the relation between linear n-widths and approximation numbers
zbMATH Open document ID: 0699.41022
DOI: 10.1016/0021-9045(89)90032-4
author: Stefan Heinrich
published in: Journal of Approximation Theory
publication date: 1989-01-01T00:00:00Z
review text: Approximation theory is one of the important branches of mathematics developing fast in different directions currently. Here the author shows that for a compact absolutely convex subset of a normal space three things coincide: the linear n-width obtained by bounded linear rank n operators, that one obtained by arbitrary linear rank n operators and the corresponding approximation number of the associated embedding. A special version of the local convexity for spaces connected with embedding operators is used. Through a counterexample it is shown that the assumption of absoluteness made on compactness cannot be replaced by relative compactness.
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 4146773
zbMATH Keywords: n-width
zbMATH Keywords: approximation number
zbMATH Keywords: local convexity
MaRDI profile type: Publication
full work available at URL: 0021-9045(89)90032-4
OpenAlex ID: W2087078181
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description: scientific article; zbMATH DE number 4146773