### Abstract

Results by Cuntz and Kreiger on uniqueness, simplicity and the ideal structure of the algebras O_{A} associated with finite matrices with entries in {0, 1} are generalized to the case where A is an infinite matrix whose rows and columns are eventually zero, but not identically zero. Similar results have been recently obtained by Kumjian, Pask, Raeburn and Renault from the viewpoint of Renault's theory of groupoids. An alternative approach, based on the realization of O_{A} as an algebra generated by a Hilbert C*-bimodule introduced by Pimsner, is proposed and compared.

Original language | English |
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Pages (from-to) | 3-18 |

Number of pages | 16 |

Journal | Journal of Operator Theory |

Volume | 45 |

Issue number | 1 |

Publication status | Published - 2001 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Kajiwara, T., Pinzari, C., & Watatani, Y. (2001). Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras.

*Journal of Operator Theory*,*45*(1), 3-18.