Narutaka Ozawa

C*-algebras and finite-dimensional approximations

Fundamental facts Basic theory: Nuclear and exact

Solid von Neumann algebras

\textrm{C}^*

Amenable actions and exactness for discrete groups

-algebras: Definitions, basic facts and examples Tensor products Constructions Exact groups and related topics Amenable traces and Kirchbergs factorization property Quasidiagonal C*-algebras AF embeddablity Local reflexivity and other tensor product conditions Summary and open problems Special topics: Simple

On a class of II1 factors with at most one Cartan subalgebra, II

\textrm{C}^*

Some prime factorization results for type II1 factors

-algebras Approximation properties for groups Weak expectation property and local lifting property Weakly exact von Neumann algebras Applications: Classification of group von Neumann algebras Herreros approximation problem Counterexamples in

On injectivity and nuclearity for operator spaces

\textrm{K}

On Ulam stability

-homology and

Weak amenability of hyperbolic groups

\textrm{K}

C*-simplicity and the unique trace property for discrete groups

-theory Appendices: Ultrafilters and ultraproducts Operator spaces, completely bounded maps and duality Lifting theorems Positive definite functions, cocycles and Schoenbergs Theorem Groups and graphs Bimodules over von Neumann algebras Bibliography Notation index Subject index.

Examples of groups which are not weakly amenable

We prove that the relative commutant of a diffuse von Neumann subalgebra in a hyperbolic group von Neumann algebra is always injective. It follows that any non-injective subfactor in a hyperbolic group von Neumann algebra is non-Gamma and prime. The proof is based on C*-algebra theory.