Eberhard Kirchberg

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Continuing the study of generalized inductive limits of finitedimensional C∗-algebras, we define a refined notion of quasidiagonality for C∗-algebras, called inner quasidiagonality, and show that a separable C∗-algebra is a strong NF algebra if and only if it is nuclear and inner quasidiagonal. Many natural classes of NF algebras are strong NF, including(More)
For a conditional expectation E on a (unital) C*-algebra A there exists a real number K ≥ 1 such that the mapping K · E − idA is positive if and only if there exists a real number L ≥ 1 such that the mapping L ·E − idA is completely positive, among other equivalent conditions. The estimate (min K) ≤ (min L) ≤ (min K)[min K] is valid, where [·] denotes the(More)
A manifold is a Poincaré duality space without singularities. McCrory obtained a homological criterion of a global nature for deciding if a polyhedral Poincaré duality space is a homology manifold, i.e. if the singularities are homologically inessential. A homeomorphism of manifolds is a degree 1 map without double points. In this paper combinatorially(More)
A C-algebra A is deened to be purely innnite if there are no characters on A, and if for every pair of positive elements a; b in A, such that b lies in the closed two-sided ideal generated by a, there exists a sequence fr n g in A such that r n ar n ! b. This deenition agrees with the usual deenition by J. Cuntz when A is simple. It is shown that the(More)