Ordered cones and approximation
type: Item
instance of: scholarly article
title: Ordered cones and approximation
zbMATH Open document ID: 0752.41033
author: Walter Roth
author: Klaus Keimel
published in: Lecture Notes in Mathematics
publication date: 1992-09-18T00:00:00Z
review text: The purpose of these lecture notes is to present a unified treatment of Korovkin type approximation theorems. Such results typically deal with certain restricted classes of linear operators on locally convex vector spaces. The authors found it necessary to leave the setting the vector spaces and turn to more general structures called locally convex cones. It was essential to include cones which are not embeddable in vector spaces. Chapter 1 is devoted to the study of locally convex cones. In Chapter 2, uniformly continuous operators and the dual cone are studied. Subcones are discussed in Chapter 3. The main results on approximation theory are presented in Chapter 4. Some research based on ideas of Nachbin is discussed in Chapter 5. Quantitative estimates for the closeness of the approximation are presented in Chapter 6. The text is clearly and concisely written. A wealth of material has been presented, much of which had previously been scattered in the literature. This book should prove invaluable to the research worker on approximation theory.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41-02
zbMATH DE Number: 53427
zbMATH Keywords: Korovkin type approximation theorems
zbMATH Keywords: locally convex cones
zbMATH Keywords: uniformly continuous operators
zbMATH Keywords: Subcones
reviewed by: H. R. Dowson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 53427