Abstract
Let A be a Banach algebra, be continuous homomorphism on A with (A) = A. The boundedlinear map D : A ! A is derivation, ifD(ab) = D(a) (b) + (a) D(b) (a; b 2 A):We say that A is -weakly amenable, when for each bounded derivation D : A ! A, there existsa 2 A such that D(a) = (a) a a (a). For a commutative Banach algebra A, we showA is weakly amenable if and only if every derivation from A into a symmetric BanachAbimodule X is zero. Also, we show that a commutative Banach algebra A is weakly amenableif and only if A# is #weakly amenable, where #(a + ) = (a) + .
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