Abstract
In this paper we consider a C*-subalgebra of the algebra of all bounded operators B(l2(X)) on the Hilbert space l2(X)) with one generating element T φ induced by a mapping φ of a 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.
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References
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Original Russian Text © S.A. Grigoryan and A.Yu. Kuznetsova, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 3, pp. 82–87.
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Grigoryan, S.A., Kuznetsova, A.Y. AF-subalgebras of a C*-algebra generated by a mapping. Russ Math. 54, 72–76 (2010). https://doi.org/10.3103/S1066369X10030102
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DOI: https://doi.org/10.3103/S1066369X10030102