Some new generalized difference spaces of nonabsolute type derived from the spaces ℓ p and ℓ ∞.

We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1≤p≤∞, respectively, and prove that ℓpλ(B) and ℓ p are linearly isomorphic for 0<p≤∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we construct the basis for the space ℓpλ(B), where 1≤p<∞. Furthermore, we determine the alpha-, beta- and gamma-duals of the space ℓpλ(B) for 1≤p≤∞. Finally, we investigate some geometric properties concerning Banach-Saks type p and give Gurarii's modulus of convexity for the normed space ℓpλ(B).