Geodesic
One class of $C^*$-algebras generated by a~family of partial isometries and multiplicators
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2012), pp. 44-55

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We consider a $C^*$-subalgebra of the algebra of all bounded operators on the Hilbert space of square-summable functions defined on some countable set. This algebra is generated by a family of partial isometries and the multiplier algebra isomorphic to the algebra of all bounded functions defined on the mentioned set. The operators of partial isometries satisfy relations defined by a prescribed map on the set. We show that the considered algebra is $\mathbb Z$-graduated. After that we construct the conditional expectation from the latter onto the subalgebra responding to zero. Using this conditional expectation, we prove that the algebra under consideration is nuclear.
Keywords: partial isometry, nuclear $C^*$-algebra, conditional expectation, completely positive map. 
@article{IVM_2012_6_a4,
     author = {A. Yu. Kuznetsova and E. V. Patrin},
     title = {One class of $C^*$-algebras generated by a~family of partial isometries and multiplicators},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {44--55},
     publisher = {mathdoc},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_6_a4/}
}
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A. Yu. Kuznetsova; E. V. Patrin. One class of $C^*$-algebras generated by a~family of partial isometries and multiplicators. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2012), pp. 44-55. http://geodesic.mathdoc.fr/item/IVM_2012_6_a4/