Lifting derivations and $n-$weak amenability of the second dual of a Banach algebra

S. Barootkoob, H. R. Ebrahimi Vishki

Published 2010-07-09, updated 2010-08-14Version 2

We show that for $n\geq 2$ the $n-$weak amenability of the second dual $\A^{**}$ of a Banach algebra $\A$ implies that of $\A$. We also provide a positive answer for the case $n=1,$ which sharpens some older results. Our method of proof also provides a unified approach to give short proofs for some known results in the case where $n=1$.