One class of C*-algebras generated by a family of partial isometries and multiplicators |
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Authors: | A Yu Kuznetsova E V Patrin |
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Institution: | 1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia
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Abstract: | 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. The algebra under consideration 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 partial isometry operators satisfy correlations defined by a prescribed map on the set. We show that the considered algebra is ?-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. |
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