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

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- by Berndt Brenken PDF
- Trans. Amer. Math. Soc.
**353**(2001), 3835-3873 Request permission

## 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.## References

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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
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1837211