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STABLE RANK FOR INCLUSIONS OF C*-ALGEBRAS

HIROYUKI OSAKA

Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga, 525-8577, Japan

https://doi.org/10.1142/S0129167X0800500XCited by:1 (Source: Crossref)

Abstract

When a unital C*-algebra A has topological stable rank one (write tsr(A) = 1), we know that tsr(pAp) = 1 for a non-zero projection p ∈ A. When, however, tsr(A) ≥ 2, it is generally false. We prove that if a unital C*-algebra A has a simple unital C*-subalgebra D of A with common unit such that D has Property (SP) and sup_{p ∈ P(D)}tsr(pAp) < ∞, then tsr(A) ≤ 2. As an application let A be a simple unital C*-algebra with tsr(A) = 1 and Property (SP), finite groups, α_k actions from G_k to Aut((⋯((A × α₁ G₁) ×_α₂ G₂)⋯) ×_{α_k-1} G_k-1). (G₀ = {1}). Then

Keywords:

AMSC: Primary 46L05, Secondary 46L08

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STABLE RANK FOR INCLUSIONS OF C*-ALGEBRAS

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