Module-Amenability on Module Extension Banach Algebras

محورهای موضوعی : History and biography

D. Ebrahimi bagha ¹ (Department of Mathematics, Faculty of Science, Islamic Azad University, Centeral Tehran Branch, P. O. Box 13185/768, Tehran, Iran)

تاریخ دریافت : 1390/10/11 تاریخ پذیرش : 1390/10/11 تاریخ انتشار : 1391/03/12

کلید واژه: module extension, Module-amenability, Banach algebras,

چکیده مقاله :

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A \oplus E$,the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equippedwith the algebras product $(a,x).(a^\prime,x^\prime)= (aa^\prime, a.x^\prime+ x.a^\prime)$. In this paper, we investigate $\triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$with the set of idempotents $E_S$, the module extension Banach algebra $S=l^1(E_S)\oplus l^1(S)$ is $\triangle$-amenable as a $l^1(E_S)$-module if and only if $l^1(E_S)$ is amenable as Banach algebra.

منابع و مأخذ:

[1] M.Amini, Module amenability for semigroup algebras, semigroup forum 69 (2004) 243-254.

[2] M.Amini and D.Ebrahimi Bagha, Weak module amenability for semigroup algebras, Semigroup forum 71 (2005). 18-26.

[3] W.G.Bade, H.G.Dales and Z.A.Lykova, Algebraic and strong splittings of extensions of Banach algebras, Mem. Amer. Math. Soc. 137, no. 656, 1999.

[4] H.G. DALES, Banach algebras and automatic continuity, London Math. Soc. Monographs, Volume 24, Clarendon press, Oxford, 2000.

[5] H.G.Dales, F. Ghahramani and N-Gronbaek, Drivations into iterated duals of Banach algebras, studia Math. 128 (1998) 19-54.

[6] J.Duncan , I.Namioka, Amenability of inverse Semigroup and their Semigroup algebras, Procedings of the Royal Society of Edinburgh 80A (1975) 309-321.

[7] D.Ebrahimi Bagha and M.Amini. Module amenability for Banach modules. CUB. A math. Journal. 13, No.02, 127-137.

[8] B.E.Johnson,Cohomology in Banach algebras,Memoirs of the American Mathematical Sosiety No,127, American Mathematical Sosiety,Providence 1972.

[9] Y.Zhang, Weak Amenability of Module extension of Banach algebras, Traps-Amer-Math. Soc. 354(2002) 4131-4151.