Ideal structure of $C^*$-algebras associated with $C^*$-correspondences

Details Ideal structure of $C^*$-algebras associated with $C^*$-correspondences Ideal structure of $C^*$-algebras associated with $C^*$-correspondences

2003-09-18

arxiv.org/abs/math/0309294v2

Mathematics

Operator Algebras

34 pages

Scientific paper

We study the ideal structure of $C^*$-algebras arising from $C^*$-correspondences. We prove that gauge-invariant ideals of our $C^*$-algebras are parameterized by certain pairs of ideals of original $C^*$-algebras. We show that our $C^*$-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert $C^*$-bimodules and relative Cuntz-Pimsner algebras are also discussed.

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