Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞ - Feyzi Başar; Ali Karaisa (The Scientific World Journal)
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 ℓp 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).