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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite sums of projections in purely infinite simple C*-algebras with torsion $ K_0$


Authors: Victor Kaftal, P. W. Ng and Shuang Zhang
Journal: Proc. Amer. Math. Soc. 140 (2012), 3219-3227
MSC (2010): Primary 46L05; Secondary 47C15
Published electronically: January 13, 2012
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Abstract: Assume that $ \mathscr {A}$ is a purely infinite simple C*-algebra whose $ K_0$ is a torsion group, namely, contains no free element. Then a positive element $ a\in \mathscr {A}$ can be written as a finite sum of projections in $ \mathscr {A}$ if and only if either $ a$ is a projection or $ \Vert a\Vert>1$.


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Additional Information

Victor Kaftal
Affiliation: Department of Mathematics, University of Cincinnati, P. O. Box 210025, Cincinnati, Ohio 45221-0025
Email: kaftalv@ucmail.uc.edu

P. W. Ng
Affiliation: Department of Mathematics, University of Louisiana, 217 Maxim D. Doucet Hall, P.O. Box 41010, Lafayette, Louisiana 70504-1010
Email: png@louisiana.edu

Shuang Zhang
Affiliation: Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025
Email: zhangs@math.uc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11152-9
PII: S 0002-9939(2012)11152-9
Received by editor(s): December 9, 2010
Received by editor(s) in revised form: March 28, 2011
Published electronically: January 13, 2012
Additional Notes: The third author was supported by a Taft Center Travel Grant when the article was presented in Beijing, China, in the summer of 2010.
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.