Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞

Abstract EN

We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0

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).