English

E_0-dilation of strongly commuting CP_0-semigroups

Operator Algebras 2008-06-04 v2

Abstract

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.

Cite

@article{arxiv.0707.1760,
  title  = {E_0-dilation of strongly commuting CP_0-semigroups},
  author = {Orr Shalit},
  journal= {arXiv preprint arXiv:0707.1760},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T08:57:31.981Z