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Ordered Cones and Approximation

  • Book
  • © 1992

Overview

Authors:
  1. Klaus Keimel
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  2. Walter Roth
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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1517)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    • Klaus Keimel, Walter Roth
    Pages 1-7

  3. Locally convex cones

    • Klaus Keimel, Walter Roth
    Pages 8-24

  4. Uniformly continuous operators and the dual cone

    • Klaus Keimel, Walter Roth
    Pages 25-54

  5. Subcones

    • Klaus Keimel, Walter Roth
    Pages 55-67

  6. Approximation

    • Klaus Keimel, Walter Roth
    Pages 68-80

  7. Nachbin cones

    • Klaus Keimel, Walter Roth
    Pages 81-105

  8. Quantitative estimates

    • Klaus Keimel, Walter Roth
    Pages 106-128

  9. Back Matter

    Pages 129-134
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Keywords

About this book

This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

Bibliographic Information

  • Book Title: Ordered Cones and Approximation

  • Authors: Klaus Keimel, Walter Roth

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0089190

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • Softcover ISBN: 978-3-540-55445-5Published: 06 May 1992

  • eBook ISBN: 978-3-540-47079-3Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 142

  • Topics: Analysis

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