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

Takeshi Katsura

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

Operator Algebras 2007-05-23 v2

Authors: Takeshi Katsura

Abstract

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.

Keywords

c*-algebras c*-correspondences ideal structure gauge-invariant ideals crossed products cuntz-pimsner algebras

Cite

@article{arxiv.math/0309294,
  title  = {Ideal structure of $C^*$-algebras associated with $C^*$-correspondences},
  author = {Takeshi Katsura},
  journal= {arXiv preprint arXiv:math/0309294},
  year   = {2007}
}

Comments

34 pages

Related papers

View all related →