On C*-Algebras Generated by the Set of Probability Distributions

In this paper, we consider $C^*$ -algebras generated by Markov operators induced by a probabilistic dynamical system. It is shown that in some cases these algebras are isomorphic to Toeplitz, Cuntz, and Cuntz–Toeplitz algebras. By the probabilistic dynamic system, the Markov operator is constructed, and it is shown that it can be extended to a quantum channel on a convex set of positive operators with unit trace.