Hilbert C*-bimodules and countably generated Cuntz-Krieger algebras

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.