Let $\cal A, \cal B$ be a non commutative Banach algebras, and $\cal A$ be weakly amenable and has a
quasi central bounded approximate identity. Let
$T:\cal A\to \cal B$ be an
algebra homomorphism which is norm decreasing and surjective. *When
ker(T) has a quasi central bounded
approximate identity?*

**In particular, when I can conclude that $\cal A/ \ker(T)$ is weakly amenable?**

Thanks!