ENGLISH

Operator-Valued Measures and Integrals for Cone-Valued Functions

By Walter Roth (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2009
ISBN
3540875646, 9783540875642
DOI
10.1007/978-3-540-87565-9
Language
english
Format
PDF
Filesize
3 MB (3004636 bytes)
Series
Lecture Notes in Mathematics 1964
Edition
1
Pages
356\369
Scanned
no
Time added
2011-06-04 13:46:07
Measure and Integration; Functional Analysis

Description

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.

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