Perturbations of Completely Positive Maps and Strong Nf Algebras
نویسنده
چکیده
Let φ : Mn → B(H) be an injective, completely positive contraction with ‖φ−1 : φ(Mn) → Mn‖cb ≤ 1 + δ(ǫ). We show that if either (i) φ(Mn) is faithful modulo the compact operators or (ii) φ(Mn) approximately contains a rank 1 projection, then there is a complete order embedding ψ : Mn → B(H) with ‖φ − ψ‖cb < ǫ. We also give examples showing that such a perturbation does not exist in general. As an application, we show that every C∗-algebra A with OL∞(A) = 1 and a finite separating family of primitive ideals is a strong NF algebra, providing a partial answer to a question of Junge, Ozawa and Ruan.
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