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 Reconstruction theorem for stationary monotone quantum Markov processes Bull. Korean Math. Soc. 2012 Vol. 49, No. 1, 63-74 https://doi.org/10.4134/BKMS.2012.49.1.63Published online January 1, 2012 Jaeseong Heo, Viacheslav P. Belavkin, and Un Cig Ji Hanyang University, University of Nottingham, Chungbuk National University Abstract : 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 Full-Text :