A Generalization of the Weak Amenability of some Banach Algebra

الأصل · EN

Let A be a Banach algebra and A** be the second dual of it. We show that by some new conditions, A is weakly amenable whenever A** is weakly amenable. We will study this problem under generalization, that is, if (n+2)-th dual of A, A⁽ⁿ⁺²⁾, is T-S-weakly amenable, then A⁽ⁿ⁾ is T-S-weakly amenable where T and S are continuous linear mappings from A⁽ⁿ⁾ into A⁽ⁿ⁾.