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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 8, pp. 1145–1151, August, 2013.
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Bhardwaj, V.K., Gupta, S. On the β-Dual of Banach-Space-Valued Difference Sequence Spaces. Ukr Math J 65, 1273–1281 (2014). https://doi.org/10.1007/s11253-014-0857-3
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DOI: https://doi.org/10.1007/s11253-014-0857-3