On type II₀E₀ -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 ⊗ L² (0, ∞)) for some separable Hilbert space K. In this paper, we define boundary weight maps through boundary weight doubles (φ{symbol}, ν), where φ{symbol} : M_n (C) → M_n (C) is a q-positive map and ν is a boundary weight over L² (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 non-cocycle conjugate E₀-semigroups for each n > 1, n ∈ N.