Derivations into Duals of Ideals of Banach Algebras

Proceedings Mathematical Sciences

T Yazdanpanah²  M E Gorgi¹ 

[1] Department of Mathematics, Faculty of Sciences, Semnan University, Semnan, Iran$$;Department of Mathematics, Teacher Training University, , Taleghani Avenue, Tehran , Iran$$

关键词: Amenability;    weak-amenability;    ideal weak-amenability.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We introduce two notions of amenability for a Banach algebra $mathcal{A}$. Let 𝐼 be a closed two-sided ideal in $mathcal{A}$, we say $mathcal{A}$ is 𝐼-weakly amenable if the first cohomology group of $mathcal{A}$ with coefficients in the dual space 𝐼* is zero; i.e., $H^1(mathcal{A},I^*) ={0}$, and, $mathcal{A}$ is ideally amenable if $mathcal{A}$ is 𝐼-weakly amenable for every closed two-sided ideal 𝐼 in $mathcal{A}$. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study the 𝐼-weak amenability of a Banach algebra $mathcal{A}$ for some special closed two-sided ideal 𝐼.

【 授权许可】

Unknown