## Abstract

An E_{0}-semigroup of B(H) is a one parameter strongly continuous semigroup of ⁎-endomorphisms of B(H) that preserve the identity. Every E_{0}-semigroup that possesses a strongly continuous intertwining semigroup of isometries is cocycle conjugate to an E_{0}-semigroup induced by the Bhat induction of a CP-flow over a separable Hilbert space K. We say an E_{0}-semigroup α is q-pure if the CP-subordinates β of norm one (i.e. ‖β_{t}(I)‖=1 and α_{t}−β_{t} is completely positive for all t≥0) are totally ordered in the sense that if β and γ are two CP-subordinates of α of norm one, then β≥γ or γ≥β. This paper shows how to construct and classify all q-pure E_{0}-semigroups induced by CP-flows over a finite-dimensional Hilbert space K up to cocycle conjugacy.

Original language | American English |
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Pages (from-to) | 1763-1867 |

Number of pages | 105 |

Journal | Journal of Functional Analysis |

Volume | 277 |

Issue number | 6 |

DOIs | |

State | Published - 15 Sep 2019 |

## Keywords

- CP-flows
- E-semigroups
- q-positive
- q-pure

## All Science Journal Classification (ASJC) codes

- Analysis