Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran


In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $n\geq 1$ implies the weak amenability of A.


[1] R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848.
[2] W.G. Bade, P.C. Curtis and H.G. Dales,, Amenability and weak amenability for Bearling and Lipschitz algebra, Proc. London Math. Soc. , 55 (1987), no. 3, 359-377.
[3] A. Bodaghi, M.Ettefagh, M.E. Gordji and A. Medghalchi, Module structures on iterated duals of Banach algebras, Constanta, 18(1) (2010) 63-80.
[4] H.G. Dales, F. Ghahramani, and N. Gronbaek, Derivations into iterated duals of Banach algebras, Studia Math, 128 (1998), no.1, 19-54.
[5] H.G. Dales, Banach algebra and Automatic continuity, Oxford university Press, (2000).
[6] M. Ettefagh, The third dual of a Banach algebra, Studia. Sci. Math. Hung, 45(1) (2008) 1-11.
[7] B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc, 127 (1972).
[8] A. Medghalchi and T.Yazdanpanah, Problems concerning n-weak amenability of a Banach algebra, Czecholovak Math. J, 55(130) (2005) 863-876.