Geodesic
On $C^*$-algebras generated by the set of probability distributions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2021), pp. 66-71

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In the paper we consider the $C^*$-algebras generated by the Markov operators, which are induced by the probabilistic dynamical system. It is shown that in some cases these algebras are isomorphic to the Toeplitz, Kunz, and Kunz-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 the unit trace.
Keywords: $C^*$-algebra, Toeplitz algebra, Cuntz algebra, quantum channel. 
@article{IVM_2021_8_a6,
     author = {G. G. Amosov and S. A. Grigoryan and A. Yu. Kuznetsova},
     title = {On $C^*$-algebras generated by the set of probability distributions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {66--71},
     publisher = {mathdoc},
     number = {8},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_8_a6/}
}
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G. G. Amosov; S. A. Grigoryan; A. Yu. Kuznetsova. On $C^*$-algebras generated by the set of probability distributions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2021), pp. 66-71. http://geodesic.mathdoc.fr/item/IVM_2021_8_a6/