  We observe that for a large class of non-amenable groups $G$, one can find
bounded representations of $A(G)$ on Hilbert space which are not completely
bounded. We also consider restriction algebras obtained from $A(G)$, equipped
with the natural operator space structure, and ask whether such algebras can be
completely isomorphic to operator algebras; partial results are obtained, using
a modified notion of Helson set which takes account of operator space
structure. In particular, we show that if $G$ is virtually abelian, then the
restriction algebra $A_G(E)$ is completely isomorphic to an operator algebra if
and only if $E$ is finite.
