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Cuntz-Krieger algebras and endomorphisms of finite direct sums of type I $_{\infty }$ factors


Author: Berndt Brenken
Journal: Trans. Amer. Math. Soc. 353 (2001), 3835-3873
MSC (1991): Primary 46LXX, 05C50
DOI: https://doi.org/10.1090/S0002-9947-01-02713-1
Published electronically: April 26, 2001
MathSciNet review: 1837211
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Abstract:

A correspondence between algebra endomorphisms of a finite sum of copies of the algebra of all bounded operators on a Hilbert space and representations of certain norm closed $\ast $-subalgebras of bounded operators generated by a finite collection of partial isometries is introduced. Basic properties of this correspondence are investigated after developing some operations on bipartite graphs that usefully describe aspects of this relationship.


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Additional Information

Berndt Brenken
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada
Email: bbrenken@math.ucalgary.ca

DOI: https://doi.org/10.1090/S0002-9947-01-02713-1
Received by editor(s): May 21, 1999
Received by editor(s) in revised form: January 20, 2000
Published electronically: April 26, 2001
Additional Notes: The author acknowledges support, in connection with this research, from the Natural Sciences and Engineering Research Council of Canada
Article copyright: © Copyright 2001 American Mathematical Society

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