Weakly Amenable

The notion of weak amenability was first introduced by Bade et al. (1987), who termed a commutative Banach algebra "weakly amenable" if every continuous derivation from into a symmetric Banach -bimodule is zero. But this is equivalent to ,and one may apply this latter condition as the definition of weak amenability for an arbitrary Banach algebra. So a Banach algebra is said to be weakly amenable if every bounded derivation from into its dual is inner (Helemskii 1989).

It is known that every -algebra is weakly amenable (Haagerup 1983).