Operator-Valued Measures and Integrals for Cone-Valued Functions

✍ Scribed by Walter Roth (auth.)

• Book ID: 127454503
• Publisher: Springer
• Year: 2009
• Tongue: English
• Weight: 3 MB
• Edition: 1
• Category: Library
• City: [Berlin]
• ISBN: 3540875654
• ISSN: 0075-8434
• DOI: 10.1007/978-3-540-87565-9

✦ 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.

✦ Subjects

Functional Analysis