Choi, Yemon and Samei, Ebrahim
(2013)
*Quotients of Fourier algebras, and representations which are not completely bounded.*
Proceedings of the American Mathematical Society, 141 (7).
pp. 2379-2388.
ISSN 0002-9939

## Abstract

We observe that for a large class of non-amenable groups G, one can find bounded representations of A(G) on a 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 the Helson set which takes into account operator space structure. In particular, we show that when G is virtually abelian and E is a closed subset, the restriction algebra AG(E) is completely isomorphic to an operator algebra if and only if E is finite.