On the β-Dual of Banach-Space-Valued Difference Sequence Spaces - Bhardwaj, V. K.; Gupta, S. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
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.