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ISSN 1088-6826(e) ISSN 0002-9939(p)

Toeplitz algebras on discrete abelian quasily ordered groups

Author(s): Xu Qingxiang
Journal: Proc. Amer. Math. Soc. 128 (2000), 1405-1408.
MSC (1991): Primary 47B35
Posted: August 5, 1999
MathSciNet review: 1654060
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Abstract: In this note, Toeplitz operators on discrete abelian quasily ordered groups are studied, and a theorem of R. Douglas is generalized.

References:

1.: E. Park, Index theory and Toeplitz algebras on certain cones in $Z^{2}$ , J. Operator Theory 23 (1990), 125-146. MR 91i:47039
2.: R. Douglas, Another look at real-valued index theory, Proceedings of Special Year on Operator Theory, Bloomington (1985-86).
3.: G. Murphy, Ordered groups and Toeplitz algebras, J. Operator Theory 18 (1987), 303-326. MR 89f:46132
4.: -, Spectral and index theory for Toeplitz operators, Proc. Royal Irish Acad., 91 (A) (1991), 1-6. MR 93k:47039
5.: N. Wegge-Olsen, $K$ -theory and $C^{*}$ -algebra, Oxford University Press Inc., New York, 1993. MR 95c:46116
6.: G. Pedersen, $C^{*}$ -algebras and their automorphism groups, Academic Press, London, 1979.
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8.: Q. Xu and X. Chen, A note on Toeplitz operators on discrete groups, Proc. Amer. Math. Soc. 126 (1998), no. 12, 3625-3631. CMP 98:17
9.: -, Toeplitz $C^{*}$ -algebras on ordered groups and their ideals of finite elements, Proc. Amer. Math. Soc. 127 (1999), no. 2, 553-561. CMP 98:05
10.: X. Chen and Q. Xu, Toeplitz operators on discrete abelian groups, preprint.

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Additional Information:

Xu Qingxiang
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234, People's Republic of China
Email: mathsci@shtu.edu.cn

DOI: 10.1090/S0002-9939-99-05268-5
PII: S 0002-9939(99)05268-5
Keywords: Discrete abelian group, quasily ordered group, Toeplitz operator
Received by editor(s): February 20, 1998
Received by editor(s) in revised form: June 30, 1998
Posted: August 5, 1999
Additional Notes: This project was partially supported by the National Natural Science Foundation of China (No. 19901019) and the Youth Science Foundation of Shanghai Higher Education (No. 98QN75).
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

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