Integral representation theorems in partially ordered vector spaces
Copyright policy )Integral representation theorems in partially ordered vector spaces
AbstractDefining 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 inC* -algebras (especially inW* -algebras andAW* -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.
quantum probability, Jordan algebras, Set functions, measures and integrals with values in ordered spaces, operator-valued Borel measure, operator Feynman-Kac formula, Riesz representation theorem, partially ordered vector space, \(C^*\)-algebras, involutory \(O^*\)-algebras, Vector-valued set functions, measures and integrals, Alexandroff representation theorem, \(\sigma\)-measure, Vector-valued measures and integration, semifields, integration process
quantum probability, Jordan algebras, Set functions, measures and integrals with values in ordered spaces, operator-valued Borel measure, operator Feynman-Kac formula, Riesz representation theorem, partially ordered vector space, \(C^*\)-algebras, involutory \(O^*\)-algebras, Vector-valued set functions, measures and integrals, Alexandroff representation theorem, \(\sigma\)-measure, Vector-valued measures and integration, semifields, integration process
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