On the B-difference sequence space derived by generalized weighted mean and compact operators

In the present paper, by using generalized weighted mean and difference matrix B, we introduce the paranormed sequence space ℓ(u,v,p;B) which consist of all sequences whose generalized weighted B-difference means are in the linear space ℓ(p) introduced by I.J. Maddox. Also, we give the basis of this space and compute its α-, β- and γ-duals. Further, we characterize the classes of matrix mappings from ℓ(u,v,p;B) to ℓ∞, c and c0. Finally, we apply the Hausdorff measure of noncompactness to characterize some classes of compact operators given by matrices on the space ℓp(u,v;B) (1⩽p<∞).