Abstract
Based on the Hilbert C ⁎ -module structure we study non-stationary monotone quantum stochastic processes and general Markov processes constructed from quantum dynamical hemigroups indexed by a totally ordered set. We prove that the quantum stochastic monotone process implementing the weakly covariant process described by a covariant quantum dynamical hemigroup with respect to a symmetry semigroup is again covariant in the strong sense.
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