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- Bruce Blackadar, Eberhard Kirchberg, EBERHARD KIRCHBERG
- 2001

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)

- Alfred K. Louis, Ulf Rehmann, +19 authors Lutz Mattner
- 2014

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)

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)

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)

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 countable 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)

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

We carefully define and study C∗-algebras over topological spaces, possibly non-Hausdorff, and review some relevant results from point-set topology 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)

- E Kirchberg
- Schriftenreihe des Vereins für Wasser-, Boden…
- 1969