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

 

Linear functionals on the Cuntz algebra


Author: Eui-Chai Jeong
Journal: Proc. Amer. Math. Soc. 134 (2006), 99-104
MSC (2000): Primary 46L05; Secondary 46L40
Published electronically: August 22, 2005
MathSciNet review: 2170548
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Abstract: For a pure state $p'$ on $\mathcal{O}_n$, which is an extension of a pure state $p$ on $\mathrm{UHF}_n$ with the property that if $(\mathcal{H}_{p'},\pi_{p'},\omega_{p'})$is a corresponding representation, then $\pi_{p'}(\mathrm{UHF}_n)=B(\mathcal{H}_{p'})$, $p'$ induces a unital shift of $B(\mathcal{H})$ of the Powers index $n$. We describe states $p$ on $\mathrm{UHF}_n$ by using sequences of unit vectors in $\mathbb{C} ^n$. We study the linear functionals on the Cuntz algebra $\mathcal{O}_n$ whose restrictions are the product pure state on $\mathrm{UHF}_n$. We find conditions on the sequence of unit vectors for which the corresponding linear functionals on $\mathcal{O}_n$become states under these conditions.


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Additional Information

Eui-Chai Jeong
Affiliation: Department of Mathematics, Chung-Ang University, Dongjak-ku, Seoul, 156-756, South Korea
Email: jeong@cau.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07886-X
PII: S 0002-9939(05)07886-X
Received by editor(s): October 25, 2000
Published electronically: August 22, 2005
Additional Notes: This work was supported by the Brain Korea 21 Project
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.