Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group $\Gamma$ admits a special linear representation with non-amenable $R$-Zariski closure if and only if it acts on an Abelian group $A$ (of...

In the paper [5] L. Drewnowski and the author proved that if $X$ is a Banach space containing a copy of $c_0$ then $L_1(\mu ,X)$ is not complemented in $cabv(\mu ,X)$ and conjectured that the same result is true if $X$ is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if $\mu$ is a finite measure and $X$ is a Banach lattice not containing copies of $c_0$, then $L_1(\mu ,X)$ is complemented in $cabv(\mu ,X)$. Here, we show that the complementability of $L_1(\mu ,X)$ in $cabv(\mu ,X)$ together...

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${}_1$ factors with prescribed countable fundamental group.