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Izv. Vyssh. Uchebn. Zaved. Mat., 2021, Number 8, Pages 66–71 (Mi ivm9704)  

Brief communications

On $C^*$-algebras generated by the set of probability distributions

G. G. Amosovabcd, S. A. Grigoryane, A. Yu. Kuznetsovaf

a Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina str., Moscow, 119991 Russia
b Moscow Institute of Physics and Technology (state university), 9 Institutski all., Dolgoprudny, 141701 Russia
c St. Petersburg University, 7/9 Universitetskaya Emb., St. Petersburg, 199034 Russia
d Institute of Mathematics with Computational Centre of the Ufa Federal Research Centre of the Russian Academy of Sciences, 112 Chernyshevskogo str., Ufa, 450008, Russia
e Kazan State Energy University, 51 Krasnoselskaya str., Kazan 420066 Russia
f Kazan Federal Univercity, 18 Kremlevskaya str., Kazan, 420008 Russia

Abstract: 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.

DOI: https://doi.org/10.26907/0021-3446-2021-8-66-71

Full text: PDF file (362 kB)
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UDC: 517.98
Received: 24.04.2021
Revised: 24.04.2021
Accepted: 29.06.2021

Citation: G. G. Amosov, S. A. Grigoryan, A. Yu. Kuznetsova, “On $C^*$-algebras generated by the set of probability distributions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 8, 66–71

Citation in format AMSBIB
\Bibitem{AmoGriKuz21}
\by G.~G.~Amosov, S.~A.~Grigoryan, A.~Yu.~Kuznetsova
\paper On $C^*$-algebras generated by the set of probability distributions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 8
\pages 66--71
\mathnet{http://mi.mathnet.ru/ivm9704}
\crossref{https://doi.org/10.26907/0021-3446-2021-8-66-71}


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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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