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

Quotients of Fourier algebras, and representations which are not completely bounded