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

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Abstract

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.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina str., 119991, Moscow, Russia

    G. G. Amosov

  2. Moscow Institute of Physics and Technology (state university), 9 Institutski all., 141701, Dolgoprudny, Russia

    G. G. Amosov

  3. St. Petersburg University, 7/9 universitetskaya emb. st., 199034, Petersburg, Russia

    G. G. Amosov

  4. Institute of Mathematics with Computational Centre of the Ufa Federal Research Centre of the Russian Academy of Sciences, 112 Chernyshevskogo str., 450008, Ufa, Russia

    G. G. Amosov

  5. Kazan State Energy University, 51 Krasnoselskaya str., 420066, Kazan, Russia

    S. A. Grigoryan

  6. Kazan Federal University, 18 Kremlevskaya str., 420008, Kazan, Russia

    A. Yu. Kuznetsova

Authors
  1. G. G. Amosov
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  2. S. A. Grigoryan
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  3. A. Yu. Kuznetsova
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Corresponding authors

Correspondence to G. G. Amosov, S. A. Grigoryan or A. Yu. Kuznetsova.

Additional information

Communicated by A. M. Bikchentaev.

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 8, pp. 66–71.

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Amosov, G.G., Grigoryan, S.A. & Kuznetsova, A.Y. On C*-Algebras Generated by the Set of Probability Distributions. Russ Math. 65, 58–62 (2021). https://doi.org/10.3103/S1066369X21080077

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  • DOI: https://doi.org/10.3103/S1066369X21080077

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