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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 6, Pages 44–55 (Mi ivm8711)  

This article is cited in 2 scientific papers (total in 2 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.

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

Bibliographic databases:

UDC: 517.98
Received: 29.06.2011

Citation: A. Yu. Kuznetsova, E. V. Patrin, “One class of $C^*$-algebras generated by a family of partial isometries and multiplicators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 6, 44–55; Russian Math. (Iz. VUZ), 56:6 (2012), 37–47

Citation in format AMSBIB
\Bibitem{KuzPat12}
\by A.~Yu.~Kuznetsova, E.~V.~Patrin
\paper One class of $C^*$-algebras generated by a~family of partial isometries and multiplicators
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 6
\pages 44--55
\mathnet{http://mi.mathnet.ru/ivm8711}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076920}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 6
\pages 37--47
\crossref{https://doi.org/10.3103/S1066369X12060059}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866275719}


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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. 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
    2. 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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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