Geodesic
$AF$-subalgebras of a~$C^*$-algebra generated by a~mapping
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 82-87

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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. 
@article{IVM_2010_3_a9,
     author = {S. A. Grigoryan and A. Yu. Kuznetsova},
     title = {$AF$-subalgebras of a~$C^*$-algebra generated by a~mapping},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {82--87},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_3_a9/}
}
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S. A. Grigoryan; A. Yu. Kuznetsova. $AF$-subalgebras of a~$C^*$-algebra generated by a~mapping. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 82-87. http://geodesic.mathdoc.fr/item/IVM_2010_3_a9/