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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 f ^ also be the domain of the generalized difference matrix B(r,s) in the sequence space f. In this paper, the β- and γ-duals of the spaces f,fs and f ^ are determined. Furthermore, two basic results on the space f are proved, the classes (f ^:μ) and (μ:f ^) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is any given sequence space.
MSC:
40A05Convergence and divergence of series and sequences
40C05Matrix methods in summability
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