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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)

- Bruce Blackadar, Eberhard Kirchberg, EBERHARD KIRCHBERG
- 2001

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)

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 carefully define and study C *-algebras over topological spaces, possibly non-Hausdorff, and review some relevant results from point-set topol-ogy along the way. We explain the triangulated category structure on the bivariant Kasparov theory over a topological space and study the analogue of the bootstrap class for C *-algebras over a finite topological… (More)

It is shown that a separable C*-algebra is inner quasidiagonal if and only if it has a separating family of quasidiagonal irreducible representations. As a consequence, a separable C*-algebra is a strong NF algebra if and only if it is nuclear and has a separating family of quasidiagonal irreducible representations. We also obtain some permanence properties… (More)

- Andrew Ranicki, Detlev W. Hoffmann, +19 authors Sorin Popa
- 2014

- Hiroshi Ando, Eberhard Kirchberg
- J. London Math. Society
- 2016

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)

- E KIRCHBERG
- Zentralblatt für Bakteriologie : international…
- 1961

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)