Document Type : Research Paper

Authors

• A. Valadkhani ¹
• S.A.R. Hosseinioun ²

¹ University of Simon Fraser, Department of Education, Vancouver, Canada

² University of Arkansas, Department of Mathematical sciences, Fayetteville, AR 72703, USA

Abstract

For a Banach algebra $A$, $A^{″}$ is $(-1)$-Weakly amenable if $A^{\prime }$ is a Banach $A^{″}$-bimodule and $H^1(A^{″},A^{\prime })=\{0\}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A^{″}$ and the weak amenability of $A^{″}$ or $A$. Moreover, we show that the second dual of every $C^{\ast }$-algebra is $(-1)$-Weakly amenable.

Keywords

• Banach algebra
• point derivation
• (-1)-Weak amenability