Ordered Cones and Approximation

Klaus Keimel, Walter Roth (auth.)9780387554457, 0-387-55445-9, 3540554459

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.

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Table of contents :
Introduction….Pages 1-7
Locally convex cones….Pages 8-24
Uniformly continuous operators and the dual cone….Pages 25-54
Subcones….Pages 55-67
Approximation….Pages 68-80
Nachbin cones….Pages 81-105
Quantitative estimates….Pages 106-128