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

Authors: Victor Kaftal, P. W. Ng and Shuang Zhang
Journal: Proc. Amer. Math. Soc. 140 (2012), 3219-3227
MSC (2010): Primary 46L05; Secondary 47C15
Posted: January 13, 2012
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Abstract: Assume that $\mathscr {A}$ is a purely infinite simple C*-algebra whose 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 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
Posted: 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 after 28 years from publication.

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