A 1-cohomology Characterization of Property (t) in Von Neumann Algebras

A 1-COHOMOLOGY CHARACTERIZATION OF PROPERTY (T) IN VON NEUMANN ALGEBRAS by JESSE PETERSON

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups. Throughout this paper N will denote a finite von Neumann algebra with a fixed normal faithful tracial state τ .

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

Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

L 2 -rigidity in von Neumann algebras

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that ...