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