Ordered Cones and Approximation
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.