The enveloping E-semigroup of a product system

It is shown that the enveloping von Neumann algebra of the spectral C⁎-algebra of a product system admits an E-semigroup whose conjugacy class is a complete isomorphism invariant for the product system. This semigroup, called the enveloping E-semigroup, displays a Wold-type decomposition that reduces the classification problem of product systems to classification of the constituent semigroups of this decomposition.