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HILBERT C*-BIMODULES AND COUNTABLY GENERATED CUNTZ-KRIEGER ALGEBRAS

TSUYOSHI KAJIWARA, CLAUDIA PINZARI and YASUO WATATANI
Journal of Operator Theory
Vol. 45, No. 1 (Winter 2001), pp. 3-18
Published by: Theta Foundation
Stable URL: http://www.jstor.org/stable/24715280
Page Count: 16
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
HILBERT C*-BIMODULES AND COUNTABLY GENERATED CUNTZ-KRIEGER ALGEBRAS
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Abstract

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 a Hilbert C*-bimodule introduced by Pimsner, is proposed and compared.

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