We consider certain correspondences on disjoint unions Ω of circles which naturally give Hilbert C*-bimodules X over circle algebras A. The bimodules X generate C*-algebras OX which are isomorphic to a continuous version of Cuntz-Krieger algebras introduced by Deaconu using groupoid method. We study the simplicity and the ideal structure of the algebras under some conditions using (I)-freeness and (II)-freeness previously discussed by the authors. More precisely, we have a bijective correspondence between the set of closed two sided ideals of OX and saturated hereditary open subsets of Ω. We also note that a formula of K-groups given by Deaconu is given without any minimality condition by just applying Pimsner's result.
|Number of pages||25|
|Journal||Journal of the Mathematical Society of Japan|
|Publication status||Published - 2002|
- Hilbert C-bimodules
ASJC Scopus subject areas