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Operator-Valued Measures and Integrals for Cone-Valued Functions - 1 edition

Operator-Valued Measures and Integrals for Cone-Valued Functions (ISBN10: 3540875646; ISBN13: 9783540875642)
ISBN13: 978-3540875642
ISBN10: 3540875646

Summary: 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.
...show more
Summary: 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....show less

Edition/Copyright: 1
Cover:
Publisher: Springer-Verlag New York, LLC
Year Published: 2009
International: No



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