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

DOI:
https://doi.org/10.1090/S0002-9939-05-07886-X

Published electronically:
August 22, 2005

MathSciNet review:
2170548

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Abstract: For a pure state on , which is an extension of a pure state on with the property that if is a corresponding representation, then , induces a unital shift of of the Powers index . We describe states on by using sequences of unit vectors in . We study the linear functionals on the Cuntz algebra whose restrictions are the product pure state on . We find conditions on the sequence of unit vectors for which the corresponding linear functionals on 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:
https://doi.org/10.1090/S0002-9939-05-07886-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.