We prove that every strongly commuting pair of CP0-semigroups has a minimal E0-dilation. This is achieved in two major steps, interesting in themselves: (1) we show that a strongly commuting pair of CP0-semigroups can be represented via a two parameter product system representation; (2) we prove that every fully coisometric product system representation has a fully coisometric, isometric dilation. In particular, we obtain that every commuting pair of CP0-semigroups on B (H), H finite-dimensional, has an E0-dilation.
- Completely contractive covariant representation
- Product system
- Strong commutativity
- Two-parameter semigroups
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