Аннотации:
In this paper, we consider $C^*$-algebrasgenerated by Markov operators induced by aprobabilistic dynamical system. It is shown that in some cases thesealgebras are isomorphic to Toeplitz, Cuntz, and Cuntz–Toeplitzalgebras. By the probabilistic dynamic system, the Markov operatoris constructed, and it is shown that it can be extended to a quantumchannel on a convex set of positive operators with unittrace.