On the <em class="a-plus-plus">β</em>-Dual of Banach-Space-Valued Difference Sequence Spaces

Abstract

The main object of the paper is to introduce Banach-space-valued difference sequence spaces ℓ _∞(X, Δ), c(X, Δ); and c₀(X, Δ) as a generalization of the well-known difference sequence spaces of Kizmaz. We obtain a set of sufficient conditions for (A _k ) ∈ E ^β (X, Δ); where E ∈ {ℓ _∞, c, c ₀} and (A _k ) is a sequence of linear operators from a Banach space X into another Banach space Y: Necessary conditions for (A _k ) ∈ E ^β (X, Δ) are also investigated.