l^p, 1 £ p < ¥, is closed linear span of its idempotents z_n(k) = d_nk , n,k Î N. Suppose that e is an idempotent of l^p,  X is a symmetric Banach l^p-module , and D: A ® X is a continuous derivation. Then De = D(e²) = 2eD(e) and so De = (De - 2eDe) - 2e(De - 2eDe) = 0. It follows that D = 0. So that l^p is weakly amenable. But l^p, 1 £ p < ¥ has no bounded approximate identity ( see ba41.dvi in the case p = 2 ), so that A is not amenable (cf. [ B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972)]).