Some Properties of Tracially Quasidiagonal Extensions.

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 K0, K1 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 p¯∈A/I (any unitary u¯∈A/I, there exists a projection p ∈ A (a unitary u ∈ A) such that |τ(p¯)=τ(π(p))|<∈(|τ(u¯)=τ(π(u))|<∈). [ABSTRACT FROM AUTHOR]