On Some Properties of Difference Operator with Some Characterizations

In this paper, we introduce the generalized spaces of the form ℋ(f, g, Δ_n^m), where ℋ represents one of the spaces ℓ_∞, c or c₀.The köthe duals corresponding to these spaces will be computed and construction of the Schauder bases for ℋ ∈ {c, c₀} will be given. Also, some matrix characterizations concerning these spaces will be computed. Moreover, the characterization of some classes of compact operators on the spaces ℓ_∞(f, g, Δ_n^m)and c₀(f, g, Δ_n^m)by employing the Hausdorff measure of non-compactness will be determined.