Operator ultra-amenability

Extending M. Daws’ definition of ultra-amenable Banach algebras, we introduce the notion of operator ultra-amenability for completely contractive Banach algebras. For a locally compact group G , we show that the operator ultra-amenability of A ( G ) imposes severe restrictions on G . In particular, it forces G to be a discrete, amenable group with no infinite abelian subgroups. For various classes of such groups, this means that G is finite.