Some Properties of Tracially Quasidiagonal Extensions

Abstract

Suppose that 0 → I → A → A/I → 0 is a tracially quasidiagonal extension of C* -algebras. In this paper, the authors give two descriptions of the K ₀, K ₁ index maps which are induced by the above extension and show that for any ϵ > 0, any τ in the tracial state space of A/I and any projection $\bar p \in A/I$ (any unitary $\bar u \in A/I$, there exists a projection p ∈ A (a unitary u ∈ A) such that $|\tau (\bar p) = \tau (\pi (p))| < \in (|\tau (\bar u) = \tau (\pi (u))| < \in )$.

Keywords

Tracially topological rank / Quasidiagonal extension / Tracially quasidiagonal extension

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