On $n$-weak biamenability of Banach algebras

Document Type : Research Paper


Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.



In this paper,  the notion of $n$-weak biamenability of Banach algebras is introduced and for every $n\geq 3$, it is shown that $n$-weak biamenability of the second dual $A^{**}$ of a Banach algebra $A$ implies $n$-weak biamenability of $A$ and this  is true for $n=1, 2$ under some mild conditions.   As a concrete example,  it is  shown that for every abelian locally compact group $G$, $L^1(G)$ is $1$-weakly biamenable and  $\ell^1(G)$ is $n$-weakly biamenable for every odd integer $n$.


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