On some Lambda–Pascal sequence spaces and compact operators

Abstract

We introduce Lambda–Pascal sequence spaces ℓq(G), c0(G), c(G) and ℓ∞(G) generated by the matrix G which is obtained by the product of Pascal matrix and Λ-matrix. It is proved that the Lambda–Pascal sequence spaces ℓq(G), c0(G), c(G) and ℓ∞(G) are BK-spaces and linearly isomorphic to ℓq, c0, c and ℓ∞, respectively. We construct Schauder bases and obtain α-, β- and γ-duals of the new spaces. We state and prove characterization theorems related to matrix transformation from the space ℓq(G) to the spaces ℓ∞, c and c0. Finally, we determine necessary and sufficient conditions for a matrix operator to be compact from the space c0(G) to any one of the spaces ℓ∞, c, c0 or ℓ1.