A generalization of almost convergence, completeness of some normed spaces with wuC series and a version of Orlicz-Pettis theorem

Karakus, MahmutBasar, Feyzi2024-08-042024-08-0420191578-73031579-1505https://doi.org/10.1007/s13398-019-00701-9https://hdl.handle.net/11616/98863In this study, we give a slight generalization of almost convergence and introduce some new multiplier spaces associated to a series k xk in a normed space X by means of this new summability method. We also obtain some characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in X and X *, respectively. Finally, we give a version of the Orlicz-Pettis theorem, as an application of this new method and an unconditionally convergent series k xk in a normed space X.eninfo:eu-repo/semantics/closedAccessAlmost convergencewuC seriesuc seriesOrlicz-Pettis theoremA generalization of almost convergence, completeness of some normed spaces with wuC series and a version of Orlicz-Pettis theoremArticle11343461347510.1007/s13398-019-00701-92-s2.0-85068745259Q1WOS:000483725900035Q1