Abstract: A group has property (T) if its trivial representation is
isolated in the unitary dual. This is equivalent to saying that any action
by affine isometries on a Hilbert space has a fixed point. A group is
called aTmenable if it admits a proper action on a Hilbert space. We shall
review those properties and see what happens when we replace the Hilbert
space by an ell^p space.
