2018/07/25 by Christopher Jankowski, Jankowski, Christopher, Daniel Markiewicz +3
Mathematics · #46L55 #46L57 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55 #msc:46L57
paper · pdf · doi:10.48550/arxiv.1807.09824
66 pages
arxiv created 2018/07/25 · openalex publication_date 2018/07/25 · arxiv updated 2018/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. \Vertβt(I)\Vert = 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.