Ordered Cones and Approximation

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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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.

• Locally Convex Cones
• Ordered Cones
• Vector space
• approximation
• approximation theory
• boundary element method
• form
• function
• functional
• functional analysis
• functions
• stochastic process
• stochastic processes
• theorem

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