%0 Journal Article
%T Sigma-weak amenability of Banach algebras
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Yazdanpanah, T.
%A Mozzami Zadeh, I.
%D 2013
%\ 01/01/2013
%V 4
%N 1
%P 66-73
%! Sigma-weak amenability of Banach algebras
%K Banach algebra
%K -derivation
%K weak amenability
%R 10.22075/ijnaa.2013.28
%X 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) + .
%U https://ijnaa.semnan.ac.ir/article_28_0ec73acaf4acf95cbff958392ec4552b.pdf