The ideal property in crossed products

Author:
Cornel Pasnicu

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2103-2108

MSC (2000):
Primary 46L05; Secondary 46L55

DOI:
https://doi.org/10.1090/S0002-9939-03-07032-1

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 -algebras by discrete, amenable groups; some applications are also given. We prove that the crossed product of a -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

Email:
cpasnic@upracd.upr.clu.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-07032-1

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