Geodesic
$C^*$-Algebras Generated by Mappings
Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 694-703

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In the paper, some properties of a singly generated $C^*$-subalgebra of the algebra of all bounded operators $B(l^2(X))$ on the Hilbert space $l^2(X)$ with the generator $T_\varphi$ induced by a mapping $\varphi$ of an infinite set $X$ into itself are investigated. A condition on $\varphi$ is presented under which the operator $T_\varphi$ is continuous, and it is proved that, if this is the case, then the study of these algebras can be reduced to that of $C^*$-algebras generated by a finite family of partial isometries of a special form. A complete description of the $C^*$-algebras generated by an injective mapping on $X$ is given. Examples of $C^*$-algebras generated by noninjective mappings are treated.
Keywords: C^*$-algebra, $C^*$-algebra generated by a mapping, injective mapping, partial isometry, Toeplitz algebra, Cuntz algebra. 
@article{MZM_2010_87_5_a4,
     author = {S. A. Grigoryan and A. Yu. Kuznetsova},
     title = {$C^*${-Algebras} {Generated} by {Mappings}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {694--703},
     publisher = {mathdoc},
     volume = {87},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a4/}
}
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S. A. Grigoryan; A. Yu. Kuznetsova. $C^*$-Algebras Generated by Mappings. Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 694-703. http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a4/