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, cilt.113, ss.3461-3475, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 113 Konu: 4
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s13398-019-00701-9
  • Dergi Adı: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Sayfa Sayıları: ss.3461-3475

Özet

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.