General inverse theorems for the best approximation in Banach spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 0991.41019
author: Toshihiko Nishishiraho
publication date: 2002-08-25T00:00:00Z
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 1667878
zbMATH Keywords: Bernstein-Zygmund theorems
zbMATH Keywords: Banach spaces
MaRDI profile type: Publication
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title: General inverse theorems for the best approximation in Banach spaces
review text: Classical theorems by Bernstein and Zygmund conclude the smoothness (i.e., differentiability and moduli of continuity) of a periodic function, \(f\), from the rapidity of the convergence to 0 of the distance from \(f\) to \(T_n\) the trigonometric functions of degree at most \(n\). To prove an analogous result in a Banach space, \(M\), this paper assumes the existence of a nested sequence of subspaces, \(M_n\), such that \(\cup M_n\) is dense in \(M\). The differentiable functions are replaced by functions in the domain of operators that map \(M_n\) into itself. An application is made to sequences of projections that are total, fundamental, and mutually orthogonal.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00060].
reviewed by: Daniel Wulbert
description: scientific article; zbMATH DE number 1667878