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Studies the partially ordered set of quantum dynamical semigroups dominated by a given semigroup on the algebra of bounded operators on a Hilbert space. For semigroups of $*$-endomorphisms, this title describes this set through cocycles to help us to prove a factorization theorem for dilations.
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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