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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2015, Volume 157, Book 1, Pages 51–59 (Mi uzku1293)  

On the ideals of $C^*$-algebra generated by a family of partial isometries and multipliers

A. Yu. Kuznetsova, E. V. Patrin

Institute of Physics, Kazan (Volga region) Federal University, Kazan, Russia

Abstract: $C^*$-subalgebra of the algebra of all bounded operators on the Hilbert space $l^2$ generated by the multiplier algebra and a family of partial isometries satisfying some relations is covered in the paper. The ideals of the algebra under study, as well as the ideals of the quotient algebra, are considered over compact operators. It is demonstrated that the quotient algebra can be represented as a direct sum of two principal ideals and has nontrivial center.

Keywords: $C^*$-algebra, partial isometry, principal ideal, central projection, Calkin algebra.

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UDC: 517.98
Received: 16.01.2015

Citation: A. Yu. Kuznetsova, E. V. Patrin, “On the ideals of $C^*$-algebra generated by a family of partial isometries and multipliers”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 157, no. 1, Kazan University, Kazan, 2015, 51–59

Citation in format AMSBIB
\Bibitem{KuzPat15}
\by A.~Yu.~Kuznetsova, E.~V.~Patrin
\paper On the ideals of $C^*$-algebra generated by a~family of partial isometries and multipliers
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2015
\vol 157
\issue 1
\pages 51--59
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1293}
\elib{https://elibrary.ru/item.asp?id=23465300}


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