Hilbert $C^{*}$ -bimodules and continuous Cuntz-Krieger algebras

2002 Journal of the Mathematical Society of Japan  
Results by Cuntz and Kreiger on uniqueness, simplicity and the ideal structure of the algebras OA 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 OA as an algebra generated by
more » ... gebra generated by a Hilbert C *bimodule introduced by Pimsner, is proposed and compared.
doi:10.2969/jmsj/1191593954 fatcat:nv3km2iqgzeippclxnbfnfz544