More on Weak Amenability of Triangular Banach Algebras

For two Banach algebras A and B and a Banach (A,B)-module X, let \mathrm{Tri}(A,X,B) be the corresponding triangular Banach algebra. In this paper, among other things, we give some characterizations of n-weak amenability of \mathrm{Tri}(A,X,B), without any assumptions on A and B. We then apply our characterizations to obtain some of the known results in the literature with fewer assumptions and provide a direct proof. To illustrate our results we present some examples, where old results in the literature are not effective in identifying their n-weak amenability.

کلیدواژه ها:

Triangular Banach algebra ، Module extension Banach algebra ، derivation ، n-weak amenability