On Popa’s factorial commutant embedding problem

On Kirchberg’s embedding problem

A C* algebra is a closed self-adjoint subalgebra of B(H), the bounded operators on a Hilbert space H. Kirchberg asked whether every C* algebra embeds into an ultrapower of a particular C* algebra, the Cuntz algebra O_2. In this talk, I will explain the model-theoretic content of this problem. In particular, I will show how model-theoretic forcing can be used to give a weak local reformulation o...

On the Embedding Problem For

The computable embedding problem

Calvert [3], [4], [5] calculated the complexity of the computable isomorphism problem for a number of familiar classes of structures. Rosendal suggested that it might be interesting to do the same for the computable embedding problem. By “computable isomorphism problem”and “computable embedding problem”we mean the di¢ culty of determining whether there exists an isomorphism (embedding) between ...

The Stable Embedding Problem

We compute a stable polynomial matrix embedding a stabilizable one. The algorithm resembles the one described by Beelen and Van Dooren for the unimodular embedding problem. We also desribe the numerical problems associated with this kind of algorithms, and point out why the stable embedding algorithm has better prospects than its unimodular counterpart.

On the Essential Commutant of T (qc)

Let T (QC) (resp. T ) be the C∗-algebra generated by the Toeplitz operators {Tφ : φ ∈ QC} (resp. {Tφ : φ ∈ L∞}) on the Hardy space H2 of the unit circle. A well-known theorem of Davidson asserts that T (QC) is the essential commutant of T . We show that the essential commutant of T (QC) is strictly larger than T . Thus the image of T in the Calkin algebra does not satisfy the double commutant r...