In this paper define the spaces l ∞ (Δ), c(Δ), and c 0 (Δ), where for instance l ∞ (Δ) = {x=(x k ):sup k |x k -x k + l |< ∞} , and compute their duals (continuous dual, α-dual, β-dual and γ-dual). We also determine necessary and sufficient conditions for a matrix A to map l ∞ (Δ) or c(Δ) into l ∞ or c , and investigate related questions.
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Hüsnü Kizmaz (1981) studied this question.