  It has been a longstanding problem whether every amenable operator algebra is
isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a
nonseparable counterexample. The existence of a separable counterexample
remains an open problem. We also initiate a general study of unitarizability of
representations of amenable groups in C*-algebras and show that our method
cannot produce a separable counterexample.
