We show that, if a Banach algebra $\A$ is a left ideal in its second dual algebra and has a left bounded approximate identity, then the weak amenability of $\A$ implies the ($2m+1$)-weak amenability of $\A$ for all $m\geq 1$.

Keywords:

$n$-weak amenability, left ideals, left bounded approximate identity $n$-weak amenability, left ideals, left bounded approximate identity

MSC Classifications:

46H20, 46H10, 46H25 show english descriptions Structure, classification of topological algebras
Ideals and subalgebras
Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 46H20 - Structure, classification of topological algebras
46H10 - Ideals and subalgebras
46H25 - Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

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