A non-stable C*-algebra with an elementary essential composition series

2017/12/06 by Ghasemi, Saeed, Koszmider, Piotr
#FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Logic (math.LO) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1712.02090

Abstract

A C*-algebra A is said to be stable if it is isomorphic to A ⊗ K(ℓ₂). Hjelmborg and Rørdam have shown that countable inductive limits of separable stable C*-algebras are stable. We show that this is no longer true in the nonseparable context even for the most natural case of an uncountable inductive limit of an increasing chain of separable stable and AF ideals: we construct a GCR, AF (in fact, scattered) subalgebra A of B(ℓ₂), which is the inductive limit of length ω₁ of its separable stable ideals I_α (α

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