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Almost convergence and generalized difference matrix. (English) Zbl 1217.40001

Summary: Let \(f\) denote the space of almost convergent sequences introduced by G. G. Lorentz [Acta Math., Uppsala 80, 167–190 (1948; Zbl 0031.29501)], and \(\hat{f}\) also be the domain of the generalized difference matrix \(B(r,s)\) in the sequence space \(f\). In this paper, the \(\beta\)- and \(\gamma \)-duals of the spaces \(f, fs\) and \(\hat{f}\) are determined. Furthermore, two basic results on the space \(f\) are proved, the classes \((\hat{f}:\mu)\) and \((\mu:\hat{f})\) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where \(\mu \) is any given sequence space.

MSC:

40A05 Convergence and divergence of series and sequences
40C05 Matrix methods for summability

Citations:

Zbl 0031.29501
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References:

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