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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 3, Pages 82–87 (Mi ivm6714)  

This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

$AF$-subalgebras of a $C^*$-algebra generated by a mapping

S. A. Grigoryana, A. Yu. Kuznetsovab

a Chair of Higher Mathematics, Kazan State Energy University, Kazan, Russia
b Chair of General Relativity and Gravitation, Kazan State University, Kazan, Russia

Abstract: In this paper we consider a $ C^*$-subalgebra of the algebra of all bounded operators $B(l^2(X))$ on the Hilbert space $l^2(X)$ with one generating element $T_\varphi$ induced by a mapping $\varphi\colon X\to X$ of the set $X$ into itself. We prove that such a $C^*$-algebra has an $AF$-subalgebra and establish commutativity conditions for the latter. We prove that a $C^*$-algebra generated by a mapping produces a dynamic system such that the corresponding group of automorphisms is invariant on elements of the $AF$-subalgebra.

Keywords: $AF$-algebra, $C^*$-algebra, partial isometry.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:3, 72–76

Bibliographic databases:

UDC: 517.98
Received: 08.07.2009

Citation: S. A. Grigoryan, A. Yu. Kuznetsova, “$AF$-subalgebras of a $C^*$-algebra generated by a mapping”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 3, 82–87; Russian Math. (Iz. VUZ), 54:3 (2010), 72–76

Citation in format AMSBIB
\Bibitem{GriKuz10}
\by S.~A.~Grigoryan, A.~Yu.~Kuznetsova
\paper $AF$-subalgebras of a~$C^*$-algebra generated by a~mapping
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 3
\pages 82--87
\mathnet{http://mi.mathnet.ru/ivm6714}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2778327}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 3
\pages 72--76
\crossref{https://doi.org/10.3103/S1066369X10030102}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649586328}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. A. Aukhadiev, S. A. Grigoryan, E. V. Lipacheva, “A compact quantum semialgebra generated by an isometry”, Russian Math. (Iz. VUZ), 55:10 (2011), 78–81  mathnet  crossref  mathscinet
    2. A. Yu. Kuznetsova, E. V. Patrin, “One class of $C^*$-algebras generated by a family of partial isometries and multiplicators”, Russian Math. (Iz. VUZ), 56:6 (2012), 37–47  mathnet  crossref  mathscinet
    3. A. Yu. Kuznetsova, “On a class of operator algebras generated by a family of partial isometries”, J. Math. Sci. (N. Y.), 216:1 (2016), 84–93  mathnet  crossref  mathscinet
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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