Weak Amenability of Banach Algebras on Locally Compact Groups

Recent work by various authors has considered the implications of Banach algebra amenability for various algebras defined over locally compact groups, one of the basic tools being the fact that a continuous homomorphic image of an amenable algebra is again amenable. In the present paper we look at the consequences of weak amenability. Here the homomorphism property fails in general, however it remains true for suitable direct summands. It is this technique that we make much use of here.