2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98260We review some of our results from the theory of product systems of Hilbert modules. We explain that the product systems obtained from a CP-semigroup in a paper by Bhat and Skeide and in a paper by Muhly and Solel are commutants of each other. Then we use this new commutant technique to construct product systems from E_0-semigroups on B^a(E) where E is a strongly full von Neumann module. (This improves the construction from a paper by Skeide for Hilbert modules where existence of a unit vector is required.) Finally, we point out that the Arveson system of a CP-semigroup constructed by Powers from two spatial E_0-semigroups is the product of the corresponding spatial Arveson systems as defined (for Hilbert modules) in a paper by Skeide. It need not coincide with the tensor product of Arveson systems.To appear in Proceedings of ``Advances in Quantum Dynamics'', Mount Holyoke, 2002Operator AlgebrasProbability46L55; 46L53; 60J25; 46L08; 81S25text