On the ideals of $C^*$-algebra generated by a family of partial isometries and multipliers
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 51-59
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$C^*$-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.
@article{UZKU_2015_157_1_a5,
author = {A. Yu. Kuznetsova and E. V. Patrin},
title = {On the ideals of $C^*$-algebra generated by a~family of partial isometries and multipliers},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {51--59},
publisher = {mathdoc},
volume = {157},
number = {1},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a5/}
}
TY - JOUR AU - A. Yu. Kuznetsova AU - E. V. Patrin TI - On the ideals of $C^*$-algebra generated by a family of partial isometries and multipliers JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2015 SP - 51 EP - 59 VL - 157 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a5/ LA - ru ID - UZKU_2015_157_1_a5 ER -
%0 Journal Article %A A. Yu. Kuznetsova %A E. V. Patrin %T On the ideals of $C^*$-algebra generated by a family of partial isometries and multipliers %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2015 %P 51-59 %V 157 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a5/ %G ru %F UZKU_2015_157_1_a5
A. Yu. Kuznetsova; E. V. Patrin. On the ideals of $C^*$-algebra generated by a family of partial isometries and multipliers. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 51-59. http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a5/