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

Karakuş M., Basar F.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.113, no.4, pp.3461-3475, 2019 (SCI-Expanded) identifier identifier


In 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.