Subproduct systems

Understand

The notion of a subproduct system, a generalization of that of a product system, is introduced.

• We show that there is an essentially 1 to 1 correspondence between cp-semigroups and pairs (X,T) where X is a subproduct system and T is an injective subproduct system representation.
• A similar statement holds for subproduct systems and units of subproduct systems.
• This correspondence is used as a framework for developing a dilation theory for cp-semigroups.