E_0-dilation of strongly commuting CP_0-semigroups
Abstract
Description
We prove that every strongly commuting pair of CP_0-semigroups has a minimal E_0-dilation. This is achieved in two major steps, interesting in themselves: 1: we show that a strongly commuting pair of CP_0-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 CP_0-semigroups on B(H), H finite dimensional, has an E_0-dilation.
45 pages; a gap in section 6 has been filled; minimality proved
45 pages; a gap in section 6 has been filled; minimality proved