Let A be a Banach algebra, be continuous homomorphism on A with (A) = A. The bounded linear map D : A ! A is derivation, if D(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 exists a 2 A such that D(a) = (a) a a (a). For a commutative Banach algebra A, we show A is weakly amenable if and only if every derivation from A into a symmetric Banach Abimodule X is zero. Also, we show that a commutative Banach algebra A is weakly amenable if and only if A# is #weakly amenable, where #(a + ) = (a) + .
Yazdanpanah, T., Mozzami Zadeh, I. (2013). Sigma-weak amenability of Banach algebras. International Journal of Nonlinear Analysis and Applications, 4(1), 66-73. doi: 10.22075/ijnaa.2013.28
MLA
T. Yazdanpanah; I. Mozzami Zadeh. "Sigma-weak amenability of Banach algebras". International Journal of Nonlinear Analysis and Applications, 4, 1, 2013, 66-73. doi: 10.22075/ijnaa.2013.28
HARVARD
Yazdanpanah, T., Mozzami Zadeh, I. (2013). 'Sigma-weak amenability of Banach algebras', International Journal of Nonlinear Analysis and Applications, 4(1), pp. 66-73. doi: 10.22075/ijnaa.2013.28
VANCOUVER
Yazdanpanah, T., Mozzami Zadeh, I. Sigma-weak amenability of Banach algebras. International Journal of Nonlinear Analysis and Applications, 2013; 4(1): 66-73. doi: 10.22075/ijnaa.2013.28
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