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On the structure of \(C^*\)-algebra generated by a family of partial isometries and multipliers. (English) Zbl 1345.46058

Summary: In the paper we consider an operator algebra generated by a family of partial isometries associated with a self-mapping on a countable set and by multipliers. An action of the unit circle on this algebra is specified that determines its \(\mathbb{Z}\)-grading. Under some conditions on the mapping the algebra is isomorphic to the crossed product of its fixed point subalgebra and the semigroup \(\mathbb{N}\).

MSC:

46L55 Noncommutative dynamical systems
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