### ON n-WEEAKLY AMENABLE BANACH ALGEBRA

#### Abstract

It is shown that if a Banach algebra A is a left ideal in its second dual algebra and has a left bounded approximate identity, then the 2-weak amenability of A implies the (2m+2)-weak amenability of A for all m ~ 1. In particular, A is 4-weakly amenable.

#### Keywords

Banach algebra, n-weakly amenable, derivation, left ideal, bounded approximate identity

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