Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 2, Pages 10–22
This article is cited in 2 scientific papers (total in 2 papers)
$C^*$-algebras generated by mappings. Criterion of irreducibility
S. A. Grigoryana, A. Yu. Kuznetsovab
a Kazan State Energy University,
51 Krasnoselskaya str., Kazan, 420066 Russia
b Kazan Federal University,
18 Kremlyovskaya str., Kazan, 420008 Russia
We study the operator algebra associated with a self-mapping $\varphi $ on a countable set $ X $ which can be represented as a directed graph. The algebra is generated by the family of partial isometries acting on the corresponding $ l^ 2(X) $. We study the structure of involutive semigroup multiplicatively generated by the family of partial isometries. We formulate the criterion when the algebra is irreducible on the Hilbert space. We consider the concrete examples of operator algebras. In particular, we give the examples of nonisomorphic $C^*$-algebras, which are the extensions by compact operators of the algebra of continuous functions on the unit circle.
$C^*$-algebra, partial isometry, positive operator, projection, compact operator, Toeplitz algebra, extension of $C^*$-algebra by compact operators.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:2, 7–18
S. A. Grigoryan, A. Yu. Kuznetsova, “$C^*$-algebras generated by mappings. Criterion of irreducibility”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 2, 10–22; Russian Math. (Iz. VUZ), 62:2 (2018), 7–18
Citation in format AMSBIB
\by S.~A.~Grigoryan, A.~Yu.~Kuznetsova
\paper $C^*$-algebras generated by mappings. Criterion of irreducibility
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\jour Russian Math. (Iz. VUZ)
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This publication is cited in the following articles:
S. A. Grigoryan, A. Yu. Kuznetsova, “$C^*$-algebras generated by mappings. Classification of invariant subspaces”, Russian Math. (Iz. VUZ), 62:7 (2018), 13–30
A. Yu. Kuznetsova, “Algebra associated with a map inducing an inverse semigroup”, Lobachevskii J. Math., 40:8, SI (2019), 1102–1112
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