J Austral Math Soc Ser A 51 pp187--215, 1991.

Integral Representation Theorems in Partially Ordered Vector Spaces

Panaiotis K. Pavlakos

Abstract

Defining a Radon-type integration process we extend the Alexandroff, Fichtengolts-Kantorovich-Hildebrandt 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.

1980 AMS Subject Classification (1985 Revision): 28B15; secondary 28B05, 46G10

Browse the article

Authors

Panaiotis K. Pavlakos

Department of Mathematics, University of Athens, Athens, Greece.