Eberhard Kirchberg

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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)
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)
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)
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)