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

 

FS-property for $C^*$-algebras


Authors: Kazunori Kodaka and Hiroyuki Osaka
Journal: Proc. Amer. Math. Soc. 129 (2001), 999-1003
MSC (1991): Primary 46L05; Secondary 46L80
Published electronically: October 10, 2000
MathSciNet review: 1814139
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Abstract:

A $C^{\ast }$-algebra $A$ is said to have the FS-property if the set of all self-adjoint elements in $A$ has a dense subset of elements with finite spectrum. We shall show that this property is not stable under taking the minimal $C^{\ast }$-tensor products even in case of separable nuclear $C^{\ast }$-algebras.


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Additional Information

Kazunori Kodaka
Affiliation: Department of Mathematical Sciences, Faculty of Science, Ryukyu University, Nishi- hara-cho, Okinawa 903-0213, Japan
Email: b985562@sci.u-ryukyu.ac.jp

Hiroyuki Osaka
Affiliation: Department of Mathematics, Ritsumeikan University, Kusatsu, Shiga, 525-8577, Japan
Email: osaka@se.ritsumei.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05712-9
PII: S 0002-9939(00)05712-9
Keywords: $C^*$-algebras, FS-property, K-groups, real rank
Received by editor(s): December 5, 1997
Received by editor(s) in revised form: June 10, 1999
Published electronically: October 10, 2000
Additional Notes: The results in this paper were presented at the Fields Institute in the program year “Operator Algebras and Applications” in 1994–1995
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society