Approximation properties for group $C\sp *$-algebras and group von Neumann algebras

Finite Generation Type Properties for Fuchsian Group Von Neumann Algebras

In this paper we prove the existence of finite systems G of generators, with special properties, for the von Neumann algebras L(Γ)⊗B(H), obtained by tensoring the group von Neumann algebra of a fuchsian group Γ with the bounded linear operators on a infinite dimensional, separable, Hilbert space H . The results show that the linear span of ordered monomials that are products of powers of adjoin...

Deformation and rigidity for group actions and von Neumann algebras

We present some recent rigidity results for von Neumann algebras (II1 factors) and equivalence relations arising from measure preserving actions of groups on probability spaces which satisfy a combination of deformation and rigidity properties. This includes strong rigidity results for factors with calculation of their fundamental group and cocycle superrigidity for actions with applications to...

The similarity problem for Fourier algebras and corepresentations of group von Neumann algebras

Let G be a locally compact group, and let A(G) and VN(G) be its Fourier algebra and group von Neumann algebra, respectively. In this paper we consider the similarity problem for A(G): Is every bounded representation of A(G) on a Hilbert space H similar to a ∗-representation? We show that the similarity problem for A(G) has a negative answer if and only if there is a bounded representation of A(...

Smooth Fourier Multipliers on Group Von Neumann Algebras

We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main result is a Hörmander-Mihlin multiplier theorem for finite-dimensional cocycles with optimal smoothness condition. We also find Littlewood-Paley type inequalities in group von Neumann algebras, prove Lp estimates for noncommutative Riesz transforms and characterize L∞ → BMO boundedness for radial Fouri...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras