Abstract
In this paper, the spaces l1(Δi3) and bv(Δi3) are introduced as the domain of generalized difference operator Δi3 of order three in the sequence spaces ℓ1 and bv. Then, some topological properties of l1(Δi3) and bv(Δi3) are given, and some inclusion relations are shown. Additionally, α−, β− and γ− dual spaces of l1(Δi3) and bv(Δi3) are computed. In the last section, the classes (μ(Δi3):λ) and (λ:μ(Δi3)) of matrix transformations are characterized where μ = {ℓ1, bv} and λ is any classical sequence space.
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