We study the partially ordered set of quantum dynamical semigroups dominated by a given semigroup on the algebra of all bounded operators on a Hilbert space. For semigroups of $*$-endomorphisms, this set can be described through cocycles. This helps us to prove a factorization theorem for dilations and to show that minimal dilations of quantum dynamical semigroups with bounded generators can be got through Hudson-Parthasarathy cocycles.
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978-0-8218-2632-4 (9780821826324)
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Schweitzer Klassifikation
Introduction Compressions and dilations Minimal dilation and induced semigroup Domination for $E_0$-semigroups Compression under domination Units Cocycle computation for CCR flows Factorization theorem Hudson-Parthasarathy cocycles Appendix A. Continuity Appendix B. Discrete case References.
