A discrete Korovkin theorem and BKW-operators
type: Item
instance of: scholarly article
title: A discrete Korovkin theorem and BKW-operators
zbMATH Open document ID: 0849.41019
author: S.-E. Takahasi
author: Ryotaro Sato
published in: Journal of Approximation Theory
publication date: 1996-06-04T00:00:00Z
review text: Using the idea of Stone-Cech compactification, the paper gives a new simple proof for a discrete Korovkin theorem, independingly considered by \textit{G. A. Anastassiou} [J. Approximation Theory 61, No. 3, 384-386 (1990; Zbl 0722.41025)] and \textit{R. Sato} [J. Approximation Theory 64, No. 2, 235-237 (1991; Zbl 0722.41026)]. Moreover, a generalization of this theorem is presented, implying some information on local unital linear contractions on the Banach space of bounded complex-valued functions \(B(X)\) on an arbitrary set \(X\). These contractions, called BKW-operators on \(B(X)\), are investigated for a finite collection of test functions with a suitable property and a seminorm defined by a finite subset of \(X\). Some examples illustrate the presented theory.
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 874150
zbMATH Keywords: Stone-Cech compactification
zbMATH Keywords: discrete Korovkin theorem
zbMATH Keywords: local unital linear contractions
zbMATH Keywords: BKW-operators
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
OpenAlex ID: W2008125982
DOI: 10.1006/JATH.1996.0023
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description: scientific article; zbMATH DE number 874150