This article is cited in 5 papers

One class of $C^*$-algebras generated by a family of partial isometries and multiplicators

A. Yu. Kuznetsova, E. V. Patrin

Chair of General Relativity and Gravitation, Kazan (Volga Region) Federal University, Kazan, Russia

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. 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.

UDC: 517.98

Received: 29.06.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:6, 37–47

Bibliographic databases:

• 
•