Mina Ettefagh

DOI Number
First page
Last page


Let A be a Banach algebra such that its (2n)−th dual for some(n ≥ 1) with first Arens product is m−weakly amenable for some (m > 2n).
We introduce some conditions by which if m is odd [even], then A is weakly [2-weakly] amenable.


Banach Algebra; Amenability; normed spaces; bilinear map.

Full Text:



M. Amyari and M. Mirzavaziri:Ideally factored algebras, Acta. Math. Acad. Paedagog. Nyha’zi (N. S.). 24 (2008), 227-233.

R. Arens: The adjoint of a bilinear operation, Proc. Amer. Math. Soc., 2 (1951), 839-848.

W. G. Bade, P. C. Curtis and H. G. Dales : Amenability and weak amenability for Bearling and Lipschitz algebra, Proc. London Math. Soc. , 55, no. 3 (1987),359-377.

S. Barootkoob and H. Ebrahimi Vishki : Lifting derivations and n−weak

amenability of the second dual of banach algebra, Bulletin of the Australian Mathematical Society, 83 (1) (2011), 122-129. doi: 10.1017/S0004972710001838.

A. Bodaghi, M. Ettefagh, M. E. Gordji , and A. Medghalchi: Module

structures on iterated duals of Banach algebras, An.st.Univ.Ovidius Constanta, 18(1) (2010), 63-80.

H. G. Dales, F. Ghahramani and N. Gronbaek : Derivations into iterated

duals of Banach algebras, Studia Math, 128, no.1 (1998), 19-54.

H. G. Dales: Banach algebra and Automatic continuity, Oxford university Press, 2000.

H. D. Dales, A. Rodriguez-Palascios and M. V. Velasco : The second

transpose of a derivation, J. London Math. Soc. (2) 64 (2001), 707-721.

M. Ettefagh: The third dual of a Banach algebra, Studia. Sci. Math. Hung, 45(1) (2008), 1-11.

M. Ettefagh: 3-Weak amenability of (2n)-th duals of Banach algebras, Colloq. Math. Vol. 128, no.1 (2012), 25-33.

A. Jabbari, A. Jabbari, M. S. Moslehian and H. R. E. Vishki : Constructions preserving n-weak amenability of Banach algebras, Mathematica Bohemica 134 (4), (2009), 349-357.

B. E. Johnson: Cohomology in Banach algebras, Mem. Amer. Math. Soc, 127 (1972).

A. Medghalchi and T. Yazdanpanah : Problems concerning n-weak amenability of a Banach algebra, Czecholovak Math. J, 55(130) (2005), 863-876.

DOI: https://doi.org/10.22190/FUMI1901001E


© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)