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The dual spaces of the sets of difference sequences of order \(m\). (English) Zbl 1132.46004
If \(x=(x_k)\) is any sequence of complex numbers, we write \(\Delta_v^m x\) for the sequence of the \(m\)th order differences of \(x\) and \(\Delta_v^m(X)=\{x=(x_k): \Delta_v^mx\in X\}\) for any set \(X\) of sequences. In this paper, we determine the \(\alpha\)-, \(\beta\)- and \(\gamma\)-duals of the sets \(\Delta_v^m(X)\) for \(X=\ell_\infty(p)\), \(c(p)\) and \(c_0(p)\). This study generalizes results of E. Malkowsky [Publ. Inst. Math., Nouv. Sér. 46(60), 97–103 (1989; Zbl 0729.46003)] in special cases.

MSC:
46A45 Sequence spaces (including Köthe sequence spaces)
40C05 Matrix methods for summability
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