n -weak amenability of a certain class of function spaces

Let A be a non-zero normed vector space and let ϕ be a non-zero element of A∗ such that ||ϕ|| ≤ 1. Assume that K = B(0) is the closed unit ball of A. According to the our recent studies on the spaces of (Cbϕ(K), || · ||∞) and (Cbϕ(K), || · ||ϕ), generated by Cb(K) and equipped with a new product “ · ” and different norms||·||∞ and ||·||ϕ, the n−weak amenability of (Cbϕ(K), ||·||∞) and (Cbϕ(K), || · ||ϕ) are investigated.