Operator-Valued Measures and Integrals for Cone-Valued Functions

✍ Scribed by Walter Roth (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2009
• Tongue: English
• Leaves: 369
• Series: Lecture Notes in Mathematics 1964
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Subjects

Measure and Integration; Functional Analysis