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,ν), where is a q-positive map and ν is a boundary weight over L2(0,∞). These doubles induce CP-flows over K for 11, n∈N.