# Weak amenability and quasi central bounded approximate identity

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!

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You might be interested in corollary 2.4 of the following article (and some of the references): arxiv.org/pdf/0902.2351.pdf –  Alvin Nov 6 '13 at 15:42
Thank u so much Alvin, You really helped me. It was true! –  Albert harold Nov 7 '13 at 20:46
I'm glad to hear it Albert:) –  Alvin Nov 8 '13 at 0:00