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Some remarks on the real rank of non-unital C*-algebras

Author(s): Takashi Sakamoto
Journal: Proc. Amer. Math. Soc. 127 (1999), 205-210.
MSC (1991): Primary 46L05
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Abstract: For a non-unital C$^{*}$-algebra $A$, let $A^{\sim }$ be the C$^{*}$-algebra obtained from $A$ by adjoining an identity. In this paper we show that

\begin{displaymath}{\text{\rm RR}}( C_{0}(X) \otimes A)={\text{\rm RR}} ( C_{0}(X) \otimes A^{\sim }) ,\end{displaymath}

where $X$ is a locally compact Hausdorff space with ${\text{\rm RR}}( C_{0}(X) ) \le 1$.

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M. Nagisa, H. Osaka and N. C. Phillips, Rank of non-commutative algebras of continuous $C^{*}$-algebra valued functions over the interval, Preliminary version.

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M. A. Rieffel, Dimension and stable rank in the K-theory of $C^{*}$-algebras, Proc. London Math. Soc. 46 (1987), 301-333. MR 84g:46085

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Additional Information:

Takashi Sakamoto
Affiliation: Department of Mathematics and Informatics, Graduate School of Science and Technology, Chiba University, 1-33, Yayoi-Cho, Inage-Ku, Chiba 263-8522, Japan
Email: msakamot@math.s.chiba-u.ac.jp

DOI: 10.1090/S0002-9939-99-05030-3
PII: S 0002-9939(99)05030-3
Keywords: C$^{*}$-algebra, real rank, stable rank
Received by editor(s): May 9, 1997
Communicated by: David R. Larson
Copyright of article: Copyright 1999, American Mathematical Society

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