Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68224120130101Sigma-weak amenability of Banach algebras66732810.22075/ijnaa.2013.28ENT.YazdanpanahDepartment of Mathematics, Persian Gulf University, Bushehr, 75168, IranI.Mozzami ZadehDepartment of Mathematics, Persian Gulf University, Bushehr, 75168, IranJournal Article20120928Let A be a Banach algebra, be continuous homomorphism on A with (A) = A. The bounded<br />linear map D : A ! A is derivation, if<br />D(ab) = D(a) (b) + (a) D(b) (a; b 2 A):<br />We say that A is -weakly amenable, when for each bounded derivation D : A ! A, there exists<br />a 2 A such that D(a) = (a) a a (a). For a commutative Banach algebra A, we show<br />A is weakly amenable if and only if every derivation from A into a symmetric Banach<br />Abimodule X is zero. Also, we show that a commutative Banach algebra A is weakly amenable<br />if and only if A# is #weakly amenable, where #(a + ) = (a) + .https://ijnaa.semnan.ac.ir/article_28_0ec73acaf4acf95cbff958392ec4552b.pdf