An abstract Radon-Nikodym theorem

AbstractIn this paper we obtain a Radon-Nikodym theorem for positive linear functionals on a B∗-algebra M. Some corollaries analogous to those obtained in the classical case are also obtained here. It is known that if X is a Banach space, then the space L1(Ω, X) of Bochner integrable functions on a probability space Ω with values in X is the completion (in a suitable topology) of the tensor product L1(Ω) ⊗ X. Using our theorem, it is possible to extend this result for certain linear mappings from M ⊗ X to X