Remarks on the modular operator and local observables

In this paper we give a characterization of the modular group of a von Neumann algebra , with a cyclic and separating vector, which provides at the same time a necessary and sufficient condition so that two von Neumann algebras ₁ and ₂, such that ₁₂, are the mutual commutants, i.e. ₁=₂.An application is made to the duality property in Quantum Field Theory, and we give a sufficient condition for PCT invariance in a theory of local observables.Partially supported by C.N.R.