Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Cuntz J., “Simple $C^*$-algebras generated by isometries”, Commun. Math. Phys., 57:2 (1977), 173–185 | DOI | MR | Zbl

[2] Cuntz J., Krieger W., “A class of $C^*$-algebras and topological Markov chains”, Invent. Math., 56:3 (1980), 251–268 | DOI | MR | Zbl

[3] Pimsner M. V., “A class of $C^*$-algebras generalizing both Cuntz–Krieger algebras and crossed products by $\mathbb Z$”, Free Probability Theory, Fields Inst. Commun., 12, Am. Math. Soc., Providence, RI, 1997, 189–212 | MR | Zbl

[4] Matsumoto K., “On $C^*$-algebras associated with subshifts”, Int. J. Math., 8:3 (1997), 357–374 | DOI | MR | Zbl

[5] Matsumoto K., “Relation among generators of $C^*$-algebras associated with subshifts”, Int. J. Math., 10:3 (1999), 385–405 | DOI | MR | Zbl

[6] Exel R., Vershik A., $C^*$-algebras of irreversible dynamical systems, 2002, 19 pp., arXiv: math/0203185v1[math.OA] | MR

[7] Arzumanyan V. A., “Operatornye algebry, assotsiirovannye s nesingulyarnymi endomorfizmami prostranstva Lebega”, Izv. AN ArmSSR, 21:6 (1986), 596–616 | MR | Zbl

[8] Grigoryan S., Kuznetsova A., “$C^*$-algebras generated by mappings”, Lobachevskii J. Math., 29:1 (2008), 5–8 | DOI | MR | Zbl

[9] Grigoryan S. A., Kuznetsova A. Yu., “$C^*$-algebry, porozhdennye otobrazheniyami”, Matem. zametki, 87:5 (2010), 694–703 | DOI | MR | Zbl

[10] Grigoryan S., Kuznetsova A., “On a category of nuclear $C^*$-algebras”, An Operator Theory Summer, Proc. 23rd Int. Conf. on Operator Theory, Theta Foundation, Bucharest, 2012, 39–50 | MR

[11] Kuznetsova A. Yu., “Ob odnom klase $C^*$-algebr, porozhdennykh schetnym semeistvom chastichnykh izometrii”, Izv. NAN Armenii. Matem., 45:16 (2010), 51–62 | MR | Zbl

[12] Kuznetsova A. Yu., Patrin E. V., “Ob odnom klasse $C^*$-algebr, porozhdennykh chastichnymi izometriyami i multiplikatorami”, Izv. vuzov. Matem., 2012, no. 6, 44–55 | MR | Zbl

[13] Johnson B. E., Parrot K. S., “Operators commuting with a von Neumann algebra modulo the set of compact operators”, J. Funct. Anal., 11:1 (1972), 39–61 | DOI | MR | Zbl

[14] Shelan S., Steprans J., “Masas in the Calkin algebra without the continuum hypothesis”, J. Appl. Anal., 17:1 (2011), 69–89 | MR