Eberhard Kirchberg

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Continuing the study of generalized inductive limits of finite-dimensional C *-algebras, we define a refined notion of quasidi-agonality 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,(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 − id A is positive if and only if there exists a real number L ≥ 1 such that the mapping L · E − id A is completely positive, among other equivalent conditions. The estimate (min K) ≤ (min L) ≤ (min K)[min K] is valid, where [·] denotes(More)
We show that nuclear C *-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C *-algebra A which is closely contained in a C *-algebra B embeds into B. The(More)
We define E-theory for separable C *-algebras over second count-able topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite approximations to this space. We obtain effective criteria for determining the invertibility of E-theory elements over(More)
I state several problems on operator algebras—mostly C*-algebras—that may be of interest to set-theorists and metric model-theorists. This list being a companion piece to [23], I frequently use [23] as a reference for standard results. I am not repeating problems stated in Weaver's survey [55] unless there is something new to say about them. Weaver and(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)
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