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

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

2010-07-09

arxiv.org/abs/1007.1649v2

Mathematics

Functional Analysis

8 pages

Scientific paper

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 $n=1$.

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