We discuss necessary as well as sufficient conditions for the second iterated local multiplier algebra of a separable C*-algebra to agree with the first.

We prove that any separable exact C*-algebra is isomorphic to a subalgebra of the Cuntz algebra O2. We further prove that if A is a simple separable unital nuclear C*-algebra, then O2 ⊗ A ∼= O2, and if, in addition, A is purely infinite, then O∞ ⊗ A ∼= A. The embedding of exact C*-algebras in O2 is continuous in the following sense. If A is a continuous field of C*-algebras over a compact manif...

In this paper, we will show that a vanishing generalized concurrence of a separable state can be seen as an algebraic variety called the Segre variety. This variety define a quadric space which gives a geometric picture of separable states. For pure, biand three-partite states the variety equals the generalized concurrence. Moreover, we generalize the Segre variety to a general multipartite sta...

We show that any non-type I separable unital AF algebra B can be modeled from inside by a nonnuclear C*-algebra and from outside by a nonexact C*-algebra. More precisely there exist unital separable quasidiagonal C*-algebras A B C of real rank zero, stable rank one, such that A is nonnuclear, C is nonexact, and both A and C are asymptotically homotopy equivalent to B. In particular A, B and C h...

Let A be a unital separable amenable quasidiagonal simple C∗-algebra with real rank zero, stable rank one, weakly unperforated K0(A) and with a unique tracial state. We show that A must have tracial rank zero. Suppose also that A satisfies the Universal Coefficient Theorem. Then A can be classified by its (ordered) K-theory up to isomorphism. In particular, A must be a simple AH-algebra with no...