Extensions of Quasidiagonal C * -algebras and K-theory
نویسنده
چکیده
Let 0 → I → E → B → 0 be a short exact sequence of C*-algebras whereE is separable, I is quasidiagonal (QD) andB is nuclear, QD and satisfies the UCT. It is shown that if the boundary map ∂ : K1(B) → K0(I) vanishes then E must be QD also. A Hahn-Banach type property for K0 of QD C ∗-algebras is also formulated. It is shown that every nuclear QD C∗-algebra has this K0Hahn-Banach property if and only if the boundary map ∂ : K1(B) → K0(I) (from above) always completely determines when E is QD in the nuclear case.
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