On Type Ii0 E0-semigroups Induced by Boundary Weight Doubles

Powers has shown that each spatial E0-semigroup can be obtained from the boundary weight map of a CP -flow acting on B(K ⊗ L(0,∞)) for some separable Hilbert space K. In this paper, we define boundary weight maps through boundary weight doubles (φ, ν), where φ : Mn(C) → Mn(C) is a q-positive map and ν is a boundary weight over L(0,∞). These doubles induce CP -flows over K for 1 < dim(K) < ∞ which then minimally dilate to E0-semigroups by a theorem of Bhat. Through this construction, we obtain uncountably many mutually noncocycle conjugate E0-semigroups for each n > 1, n ∈ N.