Operator-Valued Measures and Integrals for Cone-Valued Functions

• Κύριος συγγραφέας: Roth, Walter (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Σειρά: Lecture Notes in Mathematics, 1964
• Θέματα: Mathematics.; Functional analysis.; Measure theory.; Measure and Integration.; Functional Analysis.
• Φυσική περιγραφή: X, 356 p. online resource.
• ISBN: 9783540875659
• ISSN: 0075-8434 ;

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.