Integral representation theorems in partially ordered vector spaces

Journal of the Australian Mathematical Society

Panaiotis K. Pavlakos¹ 

关键词: 28 B 15;    secondary 28 B 05;    46 G 10;   

DOI  :  10.1017/S1446788700034194

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown