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The ideal property in crossed products

Author: Cornel Pasnicu
Journal: Proc. Amer. Math. Soc. 131 (2003), 2103-2108
MSC (2000): Primary 46L05; Secondary 46L55
Published electronically: February 5, 2003
MathSciNet review: 1963756
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Abstract: We describe the lattice of the ideals generated by projections and prove a characterization of the ideal property for ``large" classes of crossed products of commutative $C^*$-algebras by discrete, amenable groups; some applications are also given. We prove that the crossed product of a $C^*$-algebra with the ideal property by a group with the ideal property may fail to have the ideal property; this answers a question of Shuzhou Wang.

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Additional Information

Cornel Pasnicu
Affiliation: Department of Mathematics and Computer Science, University of Puerto Rico, Box 23355, San Juan, Puerto Rico 00931-3355

Keywords: $C^*$-algebra, the ideal property, crossed product
Received by editor(s): February 1, 2002
Published electronically: February 5, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society