Uniqueness up to unitary conjugacy holds for nuclear maps from separable exact C*-algebras satisfying the UCT into ultraproducts of finite factors when the maps agree on traces and total K-theory.
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Uniqueness for embeddings of nuclear $C^*$-algebras into type II$_{1}$ factors
Uniqueness up to unitary conjugacy holds for nuclear maps from separable exact C*-algebras satisfying the UCT into ultraproducts of finite factors when the maps agree on traces and total K-theory.