Journal of Operator Theory

Volume 92, Issue 1, Summer 2024 pp. 145-166.

The stable rank of a class of $C^*$-algebras with the ideal property

Authors: Qiuwen Luo
Author institution: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei 050016, China

Summary: In this paper, we prove that diagonal AH-algebras with the ideal property have stable rank one. Comparing with the result of Pasnicu (see \textit{Pacific J. Math.} \textbf{192} (2000), 159--182), our results do not require any dimension growth assumption. In the procedure of proof we give a new characterization of the ideal property for diagonal AH-algebras

DOI: http://dx.doi.org/10.7900/jot.2022aug22.2432
Keywords: stable rank one, the ideal property, diagonal $*$-homomorphism

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