Purely infinite -algebras arising from dynamical systems
Purely infinite C*-algebras from boundary actions of discrete groups.
Random matrices and -theory for exact -algebras.
Real and Complex Noncommutative Jordan Banch Algebras.
Real structure in unital separable simple -algebras with tracial rank zero and with a unique tracial state.
Relative commutant algebras of Powers' binary shifts on the hyperfinite II... factor.
Rigidity results for Bernoulli actions and their von Neumann algebras
Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II factors with prescribed countable fundamental group.
Semiregular maximal abelian *-subalgebras and the solution to the factor state Stone-Weierstrass problem.
Simplicity of the projective unitary groups defined by simple factors.
Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split W*-inclusions.
Sommes de commutateurs dans les algèbres de von Neumann finies continues
Soit une algèbre de von Neumann finie. Nous montrons que l’espace des sommes finies de commutateurs de coïncide avec le noyau de la trace centrale. Si est un facteur, il en résulte par exemple que tout élément est une combinaison linéaire finie de projecteurs de dimension . Nous montrons aussi dans ce cas que le groupe dérivé de coïncide avec le noyau du déterminant de Fuglede-Kadison.
Stability of -algebras is not a stable property.
Stable rank and real rank of compact transformation group C*-algebras
Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.
Standard and split inclusions of von Neumann algebras.
Subalgebras of a Finite Algebra.
Subtriviality of continuous fields of nuclear C*-algebras.
The action of groups on real factors of type III, .
The alternative Dunford-Pettis Property in the predual of a von Neumann algebra
Let A be a type II von Neumann algebra with predual A⁎. We prove that A⁎ does not have the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (φₙ) converging weakly to φ in A⁎ with ||φₙ|| = ||φ|| = 1 for all n ∈ ℕ and a weakly null sequence (xₙ) in A such that φₙ(xₙ) ↛ 0. This answers a question posed in [7].
The C*-algebra generated by two projections.
The Dimension Lattice of a JBW-Algebra.