A CP-semigroup is aligned if its set of trivially maximal subordinates is totally ordered by subordination. We prove that aligned spatial E0-semigroups are prime: they have no nontrivial tensor product decompositions up to cocycle conjugacy. As a consequence, we establish the existence of uncountably many noncocycle conjugate E0-semigroups of type II0 which are prime.
|Number of pages||9|
|Journal||International Mathematics Research Notices|
|State||Published - 1 Jan 2015|
ASJC Scopus subject areas
- Mathematics (all)