  We 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.
