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

 

The positivity of linear functionals on Cuntz algebras associated to unit vectors


Authors: Jung-Rye Lee and Dong-Yun Shin
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2115-2119
MSC (2000): Primary 46L30; Secondary 46L05
Published electronically: February 12, 2004
MathSciNet review: 2053984
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Abstract: We study the linear functional $\rho $ on the Cuntz algebra $\mathcal{O}_{n} $ associated to a sequence $\langle \eta _{m} \rangle $ of unit vectors $ \eta _{m}$ in $\mathbb{C}^{n} $ that is a generalization of the Cuntz state. We prove that $\rho $ is positive if and only if $\langle \eta _{m} \rangle $ is a constant sequence.


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Additional Information

Jung-Rye Lee
Affiliation: Department of Mathematics, Daejin University, Kyeonggi, 487-711, Korea
Email: jrlee@daejin.ac.kr

Dong-Yun Shin
Affiliation: Department of Mathematics, University of Seoul, Seoul, 130-743, Korea
Email: dyshin@uos.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07395-2
PII: S 0002-9939(04)07395-2
Keywords: Cuntz algebra, Cuntz state, associated linear functional
Received by editor(s): February 25, 2003
Received by editor(s) in revised form: April 17, 2003
Published electronically: February 12, 2004
Additional Notes: The second author was supported by UOS-2002
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society