• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1231-1249
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• 2005

By employing Chebotarev and Fagnola's sufficient conditions for conservativity of minimal quantum dynamical semigroups [7, 8], we construct the conservative minimal quantum dynamical semigroups generated by noncommutative elliptic operators in the sense of [2]. We apply our results to concrete examples.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.63-74
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• 2012

Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.