Ideal Amenability of Banach Algebras on Locally Compact Groups

Proceedings Mathematical Sciences

M Eshaghi Gordji²  S A R Hosseiniun¹ 

[1] Department of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran$$;Department of Mathematics, Faculty of Sciences, Semnan University, Semnan, Iran$$

关键词: Amenability;    derivation;    ideally amenable;    weak amenability.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper we study the ideal amenability of Banach algebras. Let $mathcal{A}$ be a Banach algebra and let 𝐼 be a closed two-sided ideal in $mathcal{A}, mathcal{A}$ is 𝐼-weakly amenable if $H^1(mathcal{A},I^∗)={0}$. Further, $mathcal{A}$ is ideally amenable if $mathcal{A}$ is 𝐼-weakly amenable for every closed two-sided ideal 𝐼 in $mathcal{A}$. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal amenability of Banach algebras on locally compact groups.

【 授权许可】

Unknown