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Mat. Zametki, 2010, Volume 87, Issue 5, Pages 694–703 (Mi mz3884)  

This article is cited in 7 scientific papers (total in 7 papers)

$C^*$-Algebras Generated by Mappings

S. A. Grigoryana, A. Yu. Kuznetsovab

a Kazan State Power Engineering University
b Kazan State University

Abstract: In the paper, some properties of a singly generated $C^*$-subalgebra of the algebra of all bounded operators $B(l^2(X))$ on the Hilbert space $l^2(X)$ with the generator $T_\varphi$ induced by a mapping $\varphi$ of an infinite set $X$ into itself are investigated. A condition on $\varphi$ is presented under which the operator $T_\varphi$ is continuous, and it is proved that, if this is the case, then the study of these algebras can be reduced to that of $C^*$-algebras generated by a finite family of partial isometries of a special form. A complete description of the $C^*$-algebras generated by an injective mapping on $X$ is given. Examples of $C^*$-algebras generated by noninjective mappings are treated.

Keywords: C^*$-algebra, $C^*$-algebra generated by a mapping, injective mapping, partial isometry, Toeplitz algebra, Cuntz algebra

DOI: https://doi.org/10.4213/mzm3884

Full text: PDF file (501 kB)
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English version:
Mathematical Notes, 2010, 87:5, 663–671

Bibliographic databases:

UDC: 517.986.32
Received: 22.08.2006
Revised: 30.01.2007

Citation: S. A. Grigoryan, A. Yu. Kuznetsova, “$C^*$-Algebras Generated by Mappings”, Mat. Zametki, 87:5 (2010), 694–703; Math. Notes, 87:5 (2010), 663–671

Citation in format AMSBIB
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\paper $C^*$-Algebras Generated by Mappings
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  • http://mi.mathnet.ru/eng/mz/v87/i5/p694

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. A. Aukhadiev, S. A. Grigoryan, E. V. Lipacheva, “A compact quantum semialgebra generated by an isometry”, Russian Math. (Iz. VUZ), 55:10 (2011), 78–81  mathnet  crossref  mathscinet
    2. A. Yu. Kuznetsova, E. V. Patrin, “One class of $C^*$-algebras generated by a family of partial isometries and multiplicators”, Russian Math. (Iz. VUZ), 56:6 (2012), 37–47  mathnet  crossref  mathscinet
    3. A. Yu. Kuznetsova, E. V. Patrin, “Ob idealakh $C^*$-algebry, porozhdennoi semeistvom chastichnykh izometrii i multiplikatorami”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2015, 51–59  mathnet  elib
    4. A. Yu. Kuznetsova, “On a class of operator algebras generated by a family of partial isometries”, J. Math. Sci. (N. Y.), 216:1 (2016), 84–93  mathnet  crossref  mathscinet
    5. E. V. Patrin, “O graduirovkakh $C^*$-algebry, porozhdennoi otobrazheniem i algebroi multiplikatorov”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2015, 56–66  mathnet  elib
    6. S. A. Grigoryan, A. Yu. Kuznetsova, “$C^*$-algebras generated by mappings. Criterion of irreducibility”, Russian Math. (Iz. VUZ), 62:2 (2018), 7–18  mathnet  crossref  isi
    7. S. A. Grigoryan, A. Yu. Kuznetsova, “$C^*$-algebras generated by mappings. Classification of invariant subspaces”, Russian Math. (Iz. VUZ), 62:7 (2018), 13–30  mathnet  crossref  isi
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