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Integral representation theorems in partially ordered vector spaces

Part of: Set functions, measures and integrals with values in abstract spaces Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  09 April 2009

Panaiotis K. Pavlakos
Panaiotis K. Pavlakos
Affiliation:
Department of Mathematics University of AthensAthens, Greece
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Abstract

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Defining a Radon-type integration process we extend the Alexandroff, Fichtengolts-KantorovichHildebrandt and Riesz integral representation theorems in partially ordered vector spaces.

We also identify some classes of operators with other classes of operator-valued set functions, the correspondence between operator and operator-valued set function being given by integration.

All these established results can be immediately applied in C* -algebras (especially in W* -algebras and AW* -algebras of type I), in Jordan algebras, in partially ordered involutory (O*-)algebras, in semifields, in quantum probability theory, as well as in the operator Feynman-Kac formula.

MSC classification

Secondary: 28B15: Set functions, measures and integrals with values in ordered spaces 28B05: Vector-valued set functions, measures and integrals 46G10: Vector-valued measures and integration
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 2 , October 1991 , pp. 187 - 215
Copyright
Copyright © Australian Mathematical Society 1991

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