On some spaces of summable sequences and their duals

Geraldo Soares de Souza and G. O. Golightly

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-9

Abstract:

Suppose that S is the space of all summable sequences α with ‖ α ‖ S = sup n ≥ 0 | ∑ j = n ∞ α j | and J the space of all sequences β of bounded variation with ‖ β ‖ J = | β 0 | + ∑ j = 1 ∞ | β j − β j − 1 | . Then for α in S and β in J | ∑ j = 0 ∞ α j β j | ≤ ‖ α ‖ S ‖ β ‖ J ; this inequality leads to the description of the dual space of S as J . It, related inequalities, and their consequences are the content of this paper. In particular, the inequality cited above leads directly to the Stolz form of Abel's theorem and provides a very simple argument. Also, some other sequence spaces are discussed.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:159730

DOI: 10.1155/S0161171286000091

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