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 | References | Similar Articles | Additional Information

Abstract: We study the linear functional on the Cuntz algebra associated to a sequence of unit vectors in that is a generalization of the Cuntz state. We prove that is positive if and only if 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

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