Some remarks on the real rank

of non-unital C*-algebras

Author:
Takashi Sakamoto

Journal:
Proc. Amer. Math. Soc. **127** (1999), 205-210

MSC (1991):
Primary 46L05

MathSciNet review:
1623052

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Abstract | References | Similar Articles | Additional Information

Abstract: For a non-unital C-algebra , let be the C-algebra obtained from by adjoining an identity. In this paper we show that

where is a locally compact Hausdorff space with .

**1.**Edwin J. Beggs and David E. Evans,*The real rank of algebras of matrix valued functions*, Internat. J. Math.**2**(1991), no. 2, 131–138. MR**1094700**, 10.1142/S0129167X91000089**2.**Lawrence G. Brown and Gert K. Pedersen,*𝐶*-algebras of real rank zero*, J. Funct. Anal.**99**(1991), no. 1, 131–149. MR**1120918**, 10.1016/0022-1236(91)90056-B**3.**Ryszard Engelking,*Theory of dimensions finite and infinite*, Sigma Series in Pure Mathematics, vol. 10, Heldermann Verlag, Lemgo, 1995. MR**1363947****4.**M. Nagisa, H. Osaka and N. C. Phillips,*Rank of non-commutative algebras of continuous -algebra valued functions over the interval*, Preliminary version.**5.**Marc A. Rieffel,*Dimension and stable rank in the 𝐾-theory of 𝐶*-algebras*, Proc. London Math. Soc. (3)**46**(1983), no. 2, 301–333. MR**693043**, 10.1112/plms/s3-46.2.301**6.**Shuang Zhang,*Certain 𝐶*-algebras with real rank zero and their corona and multiplier algebras. I*, Pacific J. Math.**155**(1992), no. 1, 169–197. MR**1174483**

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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:
http://dx.doi.org/10.1090/S0002-9939-99-05030-3

Keywords:
C$^{*}$-algebra,
real rank,
stable rank

Received by editor(s):
May 9, 1997

Communicated by:
David R. Larson

Article copyright:
© Copyright 1999
American Mathematical Society