Quasi-expectations and amenable von Neumann algebras

Expectations in Von Neumann Algebras

Amenable Representations and Finite Injective Von Neumann Algebras

Let U(M) be the unitary group of a finite, injective von Neumann algebra M . We observe that any subrepresentation of a group representation into U(M) is amenable in the sense of Bekka; this yields short proofs of two known results—one by Robertson, one by Haagerup—concerning group representations into U(M). A unitary representation π of a group Γ on a Hilbert space Hπ is amenable if there exis...

Representation of faithful normal expectations in von Neumann algebras

Titles and Abstracts of Talks Title: Derivations on Von Neumann Algebras and L 2 -cohomology Title: Maximal Amenable Von Neumann Subalgebras Arising from Amenable Subgroups

Consider a maximal amenable subgroup H in a discrete countable group G. In this talk I will give a general condition implying that the von Neumann subalgebra LH is still maximal amenable inside LG. The condition is expressed in terms of H-invariant measures on some compact G-space. As an example I will show that the subgroup of upper triangular matrices inside SL(n,Z) gives rise to a maximal am...

von Neumann Algebras

For every selfadjoint operator T in the Hilbert space H, f(T) makes sense not only in the obvious case where / is a polynomial but also if / is just measurable, and if fn(x)-+f(x) for all x£R (with (/,) bounded) then fn(T)-+f(T) weakly, i.e. <fn(T)£9i)+<f(T)£9ti)V£9fiCH. Moreover the set {f(T)9 f measurable} is the set of all operators S in H invariant under all unitary transformations of H whi...