Weak amenability of module extensions of Banach algebras

Zhang, Yong

doi:10.1090/S0002-9947-02-03039-8

Weak amenability of module extensions of Banach algebras
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Trans. Amer. Math. Soc. 354 (2002), 4131-4151 Request permission

Abstract:

We start by discussing general necessary and sufficient conditions for a module extension Banach algebra to be $n$-weakly amenable, for $n = 0,1,2,\cdots$. Then we investigate various special cases. All these case studies finally provide us with a way to construct an example of a weakly amenable Banach algebra which is not $3$-weakly amenable. This answers an open question raised by H. G. Dales, F. Ghahramani and N. Grønbæk.

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