Classification of q-pure q-weight maps over finite dimensional Hilbert spaces

Christopher Jankowski, Daniel Markiewicz, Robert T. Powers

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


An E0-semigroup of B(H) is a one parameter strongly continuous semigroup of ⁎-endomorphisms of B(H) that preserve the identity. Every E0-semigroup that possesses a strongly continuous intertwining semigroup of isometries is cocycle conjugate to an E0-semigroup induced by the Bhat induction of a CP-flow over a separable Hilbert space K. We say an E0-semigroup α is q-pure if the CP-subordinates β of norm one (i.e. ‖βt(I)‖=1 and αt−βt 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 E0-semigroups induced by CP-flows over a finite-dimensional Hilbert space K up to cocycle conjugacy.

Original languageEnglish
Pages (from-to)1763-1867
Number of pages105
JournalJournal of Functional Analysis
Issue number6
StatePublished - 15 Sep 2019


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

ASJC Scopus subject areas

  • Analysis


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