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 ⊗L2(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 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. © 2009 Elsevier Inc. All rights reserved.