Geodesic
Problems concerning $n$-weak amenability of a Banach algebra
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 863-876
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In this paper we extend the notion of $n$-weak amenability of a Banach algebra $\mathcal A$ when $n\in \mathbb{N}$. Technical calculations show that when $\mathcal A$ is Arens regular or an ideal in $\mathcal A^{**}$, then $\mathcal A^*$ is an $\mathcal A^{(2n)}$-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of $n$-weak amenability to $n \in \mathbb{Z}$.
In this paper we extend the notion of $n$-weak amenability of a Banach algebra $\mathcal A$ when $n\in \mathbb{N}$. Technical calculations show that when $\mathcal A$ is Arens regular or an ideal in $\mathcal A^{**}$, then $\mathcal A^*$ is an $\mathcal A^{(2n)}$-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of $n$-weak amenability to $n \in \mathbb{Z}$.
Classification : 46H20, 46H40
Keywords: Banach algebra; weakly amenable; Arens regular; $n$-weakly amenable 
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Medghalchi, Alireza; Yazdanpanah, Taher. Problems concerning $n$-weak amenability of a Banach algebra. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 863-876. http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a3/

[1] W. G. Bade, P. G. Curtis and H. G. Dales: Amenability and weak amenability for Beurling and Lipschitz algebra. Proc. London Math. Soc. 55 (1987), 359–377. | MR

[2] H. G.  Dales, F.  Ghahramanim and N.  Gronbaek: Derivations into iterated duals of Banach algebras. Studia Math. 128 (1998), 19–54. | MR

[3] H. G.  Dales, A.  Rodriguez-Palacios and M. V. Valasco: The second transpose of a derivation. J.  London Math. Soc. 64 (2001), 707–721. | DOI | MR

[4] M.  Despic and F.  Ghahramani: Weak amenability of group algebras of locally compact groups. Canad. Math. Bull. 37 (1994), 165–167. | DOI | MR

[5] J.  Duncan and Hosseiniun: The second dual of a Banach algebra. Proc. Roy. Soc. Edinburgh 84A (1978), 309–325. | MR

[6] N.  Gronbaek: Weak amenability of group algebras. Bull. London Math. Soc. 23 (1991), 231–284. | MR

[7] U.  Haagerup: All nuclear $C^*$-algebras are amenable. Invent. Math. 74 (1983), 305–319. | DOI | MR | Zbl

[8] B. E.  Johnson: Cohomology in Banach Algebras. Mem. Amer. Math. Soc. 127 (1972). | MR | Zbl

[9] B. E.  Johnson: Weak amenability of group algebras. Bull. Lodon Math. Soc. 23 (1991), 281–284. | DOI | MR | Zbl

[10] T. W.  Palmer: Banach Algebra, the General Theory of $*$-algebra. Vol.  1: Algebra and Banach Algebras. Cambridge University Press, Cambridge, 1994. | MR