Operator-valued measures and integrals for cone-valued functions

Walter Roth (auth.)9783540875642, 3540875646, 9783540875659, 3540875654

Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is used for real-valued functions and measures, whereas suprema and infima are replaced with topological limits in the vector-valued case.

A novel approach employing more general structures, locally convex cones, which are natural generalizations of locally convex vector spaces, is introduced here. This setting allows developing a general theory of integration which simultaneously deals with all of the above-mentioned cases.

Table of contents :
Front Matter….Pages i-x
Introduction….Pages 1-7
Locally Convex Cones….Pages 9-117
Measures and Integrals. The General Theory….Pages 119-248
Measures on Locally Compact Spaces….Pages 249-340
Back Matter….Pages 341-362