E_0-dilation of strongly commuting CP_0-semigroups

Details E_0-dilation of strongly commuting CP_0-semigroups E_0-dilation of strongly commuting CP_0-semigroups

2007-07-12

arxiv.org/abs/0707.1760v2

Journal of Functional Analysis, Vol. 255/1 46-89, 2008

Mathematics

Operator Algebras

45 pages; a gap in section 6 has been filled; minimality proved

Scientific paper

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.

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