Bulletin of the
Korean Mathematical Society BKMS

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.

Keywords: Hilbert $C^{*}$-module, covariant representation, quantum stochastic process, quantum dynamical semigroup

MSC numbers: Primary 60G20, 46L08; Secondary 60G10, 46L55